Chapter 10 Resource Masters - MHSchooliv Teacher’s Guide to Using the Chapter 10 Resource Masters...

Chapter 10Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission isgranted to reproduce the material contained herein on the condition that suchmaterial be reproduced only for classroom use; be provided to students, teachers,and families without charge; and be used solely in conjunction with GlencoeCalifornia Mathematics, Grade 6. Any other reproduction, for use or sale, isprohibited without prior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

ISBN: 978-0-07-878305-0MHID: 0-07-878305-4 CAGR6 CRM10

Printed in the United States of America

4 5 6 7 8 9 10 MAL 14 13 12 11 10 09

Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters

booklets are available as consumable workbooks in both English and Spanish.

MHID ISBNStudy Guide and Intervention Workbook 0-07-878871-4 978-0-07-878871-0

Skills Practice Workbook 0-07-878873-0 978-0-07-878873-4

Practice Workbook 0-07-878875-7 978-0-07-878875-8

Word Problem Practice Workbook 0-07-878877-3 978-0-07-878877-2

Spanish VersionsStudy Guide and Intervention Workbook 0-07-878872-2 978-0-07-878872-7Skills Practice Workbook 0-07-878874-9 978-0-07-878874-1Practice Workbook 0-07-878876-5 978-0-07-878876-5Word Problem Practice Workbook 0-07-878878-1 978-0-07-878878-9

Answers for Workbooks The answers for Chapter 10 of these workbooks can be found in the

back of this Chapter Resource Masters booklet.

StudentWorks Plus™ This CD-ROM includes the entire Student Edition test along with the

English workbooks listed above.

TeacherWorks Plus™ All of the materials found in this booklet are included for viewing,

printing, and editing in this CD-ROM.

Spanish Assessment Masters MHID: 0-07-878879-X ISBN: 978-0-07-878879-6

These masters contain a Spanish version of Chapter 10 Test Form 2A and Form 2C.

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Teacher’s Guide to Using the Chapter 10 Resource Masters .........................................iv

Chapter Resources Chapter 10 Student-Built Glossary ....................1Chapter 10 Family Letter (English) ....................3Chapter 10 Family Activity (English) ..................4Chapter 10 Family Letter (Spanish) ...................5Chapter 10 Family Activity (Spanish).................6Chapter 10 Anticipation Guide (English)............7Chapter 10 Anticipation Guide (Spanish) ..........8

Lesson 10-1 Angle RelationshipsLesson Reading Guide ......................................9Study Guide and Intervention ..........................10Skills Practice...................................................11Practice ............................................................12Word Problem Practice ....................................13Enrichment .......................................................14

Lesson 10-2 Complementary andSupplementary AnglesLesson Reading Guide ....................................15Study Guide and Intervention ..........................16Skills Practice...................................................17Practice ............................................................18Word Problem Practice ....................................19Enrichment .......................................................20

Lesson 10-3 Statistics: DisplayData in a Circle GraphLesson Reading Guide ....................................21Study Guide and Intervention ..........................22Skills Practice...................................................23Practice ............................................................24Word Problem Practice ....................................25Enrichment .......................................................26TI-73 Activity ....................................................27

Lesson 10-4 TrianglesLesson Reading Guide ....................................28Study Guide and Intervention ..........................29Skills Practice...................................................30Practice ............................................................31Word Problem Practice ....................................32Enrichment .......................................................33

Lesson 10-5 Problem-SolvingInvestigation: Use LogicalReasoningStudy Guide and Intervention ..........................34Skills Practice...................................................35Practice ............................................................36Word Problem Practice ....................................37

Lesson 10-6 QuadrilateralsLesson Reading Guide ....................................38Study Guide and Intervention ..........................39Skills Practice...................................................40Practice ............................................................41Word Problem Practice ....................................42Enrichment .......................................................43

Lesson 10-7 Similar FiguresLesson Reading Guide ....................................44Study Guide and Intervention ..........................45Skills Practice...................................................46Practice ............................................................47Word Problem Practice ....................................48Enrichment .......................................................49

Lesson 10-8 Polygons andTessellationsLesson Reading Guide ....................................50Study Guide and Intervention ..........................51Skills Practice...................................................52Practice ............................................................53Word Problem Practice ....................................54Enrichment .......................................................55TI-73 Activity ....................................................56

Lesson 10-9 TranslationsLesson Reading Guide ....................................57Study Guide and Intervention ..........................58Skills Practice...................................................59Practice ............................................................60Word Problem Practice ....................................61Enrichment .......................................................62Spreadsheet Activity ........................................63

Lesson 10-10 ReflectionsLesson Reading Guide ....................................64Study Guide and Intervention ..........................65Skills Practice...................................................66Practice ............................................................67Word Problem Practice ....................................68Enrichment .......................................................69TI-73 Activity ....................................................70

Chapter 10 AssessmentStudent Recording Sheet ................................71Rubric for Scoring Pre-AP................................72Chapter 10 Quizzes 1 and 2 ............................73Chapter 10 Quizzes 3 and 4 ............................74Chapter 10 Mid-Chapter Test ...........................75Chapter 10 Vocabulary Test .............................76Chapter 10 Test, Form 1 ..................................77Chapter 10 Test, Form 2A................................79Chapter 10 Test, Form 2B................................81Chapter 10 Test, Form 2C................................83Chapter 10 Test, Form 2D................................85Chapter 10 Test, Form 3 ..................................87Chapter 10 Extended-Response Test ..............89Chapter 10 Standardized Test Practice............90

Answers..................................................A1–A41

Contents

iv

Teacher’s Guide to Using the Chapter 10 Resource Masters

The Chapter 10 Resource Masters includes the core materials needed for Chapter 10. Thesematerials include worksheets, extensions, and assessment options. The answers for thesepages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing on theTeacherWorks Plus™ CD-ROM.

Chapter ResourcesStudent-Built Glossary (pages 1–2) Thesemasters are a student study tool thatpresents up to twenty of the key vocabularyterms from the chapter. Students are torecord definitions and/or examples for eachterm. You may suggest that studentshighlight or star the terms with which theyare not familiar. Give this to students beforebeginning Lesson 10-1. Encourage them toadd these pages to their mathematics studynotebooks. Remind them to complete theappropriate words as they study each lesson.

Family Letter and Family Activity(pages 3–6) The letter informs yourstudents’ families of the mathematics theywill be learning in this chapter. The familyactivity helps them to practice problems thatare similar to those on the state test. A fullsolution for each problem is included.Spanish versions of these pages are alsoincluded. Give these to students to takehome before beginning the chapter.

Anticipation Guide (pages 7–8) Thismaster, presented in both English andSpanish, is a survey used before beginningthe chapter to pinpoint what students mayor may not know about the concepts in thechapter. Students will revisit this surveyafter they complete the chapter to see iftheir perceptions have changed.

Lesson ResourcesLesson Reading Guide Get Ready for theLesson reiterates the questions from thebeginning of the Student Edition lesson.Read the Lesson asks students to interpretthe context of and relationships amongterms in the lesson. Finally, RememberWhat You Learned asks students tosummarize what they have learned usingvarious representation techniques. Use as astudy tool for note taking or as an informalreading assignment. It is also a helpful toolfor ELL (English Language Learners).

Study Guide and Intervention Thismaster provides vocabulary, key concepts,additional worked-out examples and CheckYour Progress exercises to use as areteaching activity. It can also be used inconjunction with the Student Edition as aninstructional tool for students who havebeen absent.

Skills Practice This master focuses moreon the computational nature of the lesson.Use as an additional practice option or ashomework for second-day teaching of thelesson.

Practice This master closely follows thetypes of problems found in the Exercisessection of the Student Edition and includesword problems. Use as an additionalpractice option or as homework for second-day teaching of the lesson.

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Word Problem Practice This masterincludes additional practice in solving wordproblems that apply the concepts of thelesson. Use as an additional practice or ashomework for second-day teaching of thelesson.

Enrichment These activities may extendthe concepts of the lesson, offer a historicalor multicultural look at the concepts, orwiden students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.

Graphing Calculator, ScientificCalculator, or Spreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts insome lessons of this chapter. Use as analternative approach to some concepts or asan integral part of your lesson presentation.

Assessment OptionsThe assessment masters in the Chapter 10Resource Masters offer a wide range ofassessment tools for formative (monitoring)assessment and summative (final) assessment.

Student Recording Sheet This mastercorresponds with the standardized testpractice at the end of the chapter.

Pre-AP Rubric This master providesinformation for teachers and students onhow to assess performance on open-endedquestions.

Quizzes Four free-response quizzes offerassessment at appropriate intervals in thechapter.

Mid-Chapter Test This 1-page testprovides an option to assess the first half ofthe chapter. It parallels the timing of theMid-Chapter Quiz in the Student Editionand includes both multiple-choice and free-response questions.

Vocabulary Test This test is suitable forall students. It includes a list of vocabularywords and 10 questions to assess students’knowledge of those words. This can also beused in conjunction with one of the leveledchapter tests.

Leveled Chapter Tests• Form 1 contains multiple-choice questions

and is intended for use with below gradelevel students.

• Forms 2A and 2B contain multiple-choicequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D contain free-responsequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.

• Form 3 is a free-response test for use withabove grade level students.

All of the above mentioned tests include afree-response Bonus question.

Extended-Response Test Performanceassessment tasks are suitable for allstudents. Sample answers and a scoringrubric are included for evaluation.

Standardized Test Practice These threepages are cumulative in nature. It includesthree parts: multiple-choice questions withbubble-in answer format, griddablequestions with answer grids, and short-answer free-response questions.

Answers• The answers for the Anticipation Guide

and Lesson Resources are provided asreduced pages with answers appearing in red.

• Full-size answer keys are provided for theassessment masters.

Chapter 10 1 Glencoe California Mathematics, Grade 6

NAME ________________________________________ DATE ______________ PERIOD _____

Student-Built Glossary

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Vocabulary TermFound

Definition/Description/Exampleon Page

acute angle

complementary angles

congruent angles

congruent figures

line of reflection

line of symmetry

line symmetry

obtuse angle

parallelogram

polygon

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Vocabulary TermFound

Definition/Description/Exampleon Page

quadrilateral KWAH-druh-LA-tuh-ruhl

reflection

rhombus RAHM-buhs

similar figures

straight angle

supplementary angles

tessellation

transformation

translation

trapezoid TRA-puh-ZOYD

vertex

NAME ________________________________________ DATE ______________ PERIOD _____

Student-Built Glossary (continued)10

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Family LetterNAME ________________________________________ DATE ______________ PERIOD _____


Dear Parent or Guardian:

Geometric figures can be found in all kinds of places. Wallpaper

and tile often contain geometric patterns. Traffic signs are

created in the shapes of various types of polygons. Applying

geometric concepts to the real world can help us solve many

types of problems.

In Chapter 10, Geometry: Polygons, your child will learn about

angles, circle graphs, polygons, similar figures, tessellations,

translations, and reflections. Your child will also learn to use logical

reasoning to solve problems. In the study of this chapter, your child

will complete a variety of daily classroom assignments and activities

and possibly produce a chapter project.

By signing this letter and returning it with your child, you agree

to encourage your child by getting involved. Enclosed is an

activity you can do with your child that practices how the math

we will be learning in Chapter 10 might be tested. You may

also wish to log on to ca.gr6math.com for self-check quizzes

and other study help. If you have any questions or comments,

feel free to contact me at school.

Sincerely,

Signature of Parent or Guardian ______________________________________ Date ________

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Family ActivityStandards Practice

NAME ________________________________________ DATE ______________ PERIOD _____


10

Fold the page along the dashed line. Work each problem on another piece of paper.Then unfold the page to check your work.

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1. On the coordinate axis shown below, thegeometric shape has been transformedin some way.

What word best describes thetransformation that has taken place?

A rotationB translationC reflectionD dilation

Fold here.

Solution

1. Hint: An object that has been rotated hasbeen turned around a point. An objectthat has been translated has been movedin its current form to different coordinatesin the plane. An object that has beenreflected will be a mirror image of theoriginal object over a line of reflection. Adilation results in a change in size fromthe original object.

The object has not been turned, so it isnot a rotation. The object is orienteddifferently than originally, so it cannotbe a translation. The object's size didnot change, so it cannot be a dilation.

The object is a mirror image of itself onthe other side of the x-axis, so thetransformation is a reflection.

The answer is C.

2. The following triangles are similar.

Which of the following is not true aboutsimilar figures?

A Similar figures have equalcorresponding angles.

B Similar figures have proportionalcorresponding side lengths.

C Similar figures do not have to haveproportional corresponding sidelengths.

D Similar figures are the same shapebut may be a different size.

Solution

2. Hint: Similar triangles have the sameshape and their sizes are proportional.

When two figures are similar, they arethe same shape, their correspondingsides are proportional, and correspondingangles are equal. Based on the definitionof similar figures, choices A, B, and D arealso true.

Choice C directly contradicts thedefinition of similar figures and is not true.

The answer is C.

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Carta a la familiaNOMBRE ______________________________________ FECHA ____________ PERÍODO ___

Capítulo 10 5 Glencoe California Mathematics, Grade 6

Estimado padre o apoderado:

Hay figuras geométricas por doquier. El papel tapiz y las

baldosas contienen a menudo patrones geométricos. Las señales

de tránsito se fabrican en forma de varios tipos de polígonos. La

aplicación de conceptos geométricos al mundo real puede

ayudarnos a resolver muchos tipos de problemas.

En el Capítulo 10, Geometría: Polígonoss, su hijo(a) aprenderá

sobre ángulos, gráficas circulares, polígonos, figuras semejantes,

teselados, traslaciones y reflexiones. Su hijo(a) también aprenderá

a usar el razonamiento lógico para resolver problemas. En el estu-

dio de este capítulo, su hijo(a) completará una variedad de tareas

y actividades diarias y es posible que trabaje en un proyecto del

capítulo.

Al firmar esta carta y devolverla con su hijo(a), usted se com-

promete a ayudarlo(a) a participar en su aprendizaje. Junto con

esta carta, va incluida una actividad que puede realizar con

él(ella) y la cual practica lo que podrían encontrar en las prue-

bas de los conceptos matemáticos que aprenderán en el

Capítulo 10. Además, visiten ca.gr6math.com para ver auto-

controles y otras ayudas para el estudio. Si tiene cualquier pre-

gunta o comentario, por favor contácteme en la escuela.

Cordialmente,

Firma del padre o apoderado ________________________________________ Fecha ______

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Actividad en familiaPráctica de estándares

NOMBRE ______________________________________ FECHA ____________ PERÍODO ___


1. En el plano de coordenadas siguiente, laforma geométrica se transformó dealguna manera.

¿Qué palabra describe mejor estatransformación?

A rotaciónB traslaciónC reflexiónD dilatación

Doblen aquí.

Solución

1. Ayuda: Un objeto que se ha rotado esaquél que se hace girar alrededor de unpunto. Un objeto trasladado se mueve ensu forma actual a diferentes coordenadasen el plano. Un objeto reflejado es unaimagen especular del objeto original sobreun eje de reflexión. Una dilación resulta enel cambio de tamaño del objeto original.

El objeto no se giró, de modo que no esuna rotación. El objeto se orienta demanera distinta a la original, por eso nopuede ser una traslación. Su tamaño nocambió, entonces no puede ser unadilatación.

El objeto es una imagen especular de símismo del otro lado del eje x, de modoque la transformación es una reflexión.

La respuesta es C.

2. Los siguientes triángulos son semejantes.

¿Cuál de los siguientes no cierto encuanto a figuras semejantes?

A Éstas tienen ángulos correspondien-tes iguales.

B Éstas tienen longitudes lateralescorrespondientes proporcionales.

C Éstas no necesitan tener longitudeslaterales correspondientesproporcionales.

D Éstas tienen la misma forma peropueden tener un tamaño distinto.

Solución

2. Ayuda: Los triángulos semejantes tienenla misma forma y sus tamaños sonproporcionales.

Dos figuras son semejantes cuandotienen la misma forma, son proporciona-les sus lados correspondientes y soniguales sus ángulos correspondientes. Enbase a la definición de figuras semejan-tes, las opciones A, B y D también sonciertas.

La opción C contradice directamente ladefinición de figuras semejantes y no esverdadera.

La respuesta es C.

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Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas.

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NAME ________________________________________ DATE ______________ PERIOD _____

Anticipation GuideGeometry: Polygons


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Step 2

Step 1

STEP 1 Statement STEP 2A, D, or NS A or D

1. The point where the sides of an angle meet is called the vertex.

2. An obtuse angle has a measure less than 90°.3. Two angles are complementary if the sum of their measures

is 180°.4. The percents in a circle graph total 100% and the angle

measures will total 360°.5. The sum of the measures of the angles in a triangle is 360°.6. A triangle is classified as obtuse if one angle in the triangle

is obtuse.7. All rectangles are quadrilaterals, but not all quadrilaterals

are rectangles.8. Figures that are the same shape and size are called similar

figures.9. If two figures are similar, then the corresponding angles are

congruent.10. A polygon is a two-dimensional figure with five sides.11. After a figure is translated, the resulting figure is the same

size and shape as the original.12. Only figures with at least one line of symmetry can be

transformed by a reflection.

Before you begin Chapter 10

• Read each statement.

• Decide whether you Agree (A) or Disagree (D) with the statement.

• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).

After you complete Chapter 10

• Reread each statement and complete the last column by entering an A or a D.

• Did any of your opinions about the statements change from the first column?

• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.

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NOMBRE ______________________________________ FECHA ____________ PERÍODO ___

Ejercicios preparatoriosGeometría: Polígonos

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PASO 2

Antes de comenzar el Capítulo 10

• Lee cada enunciado.

• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.

• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a).

Después de completar el Capítulo 10

• Vuelve a leer cada enunciado y completa la última columna con una A o una D.

• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?

• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.

PASO 1

PASO 1 PASO 2A, D o NS

EnunciadoA o D

1. El punto donde se encuentran los lados de un ángulo se llama vértice.

2. Un ángulo obtuso mide menos que 90°.3. Dos ángulos son complementarios si la suma de sus medidas

es 180°.4. Los porcentajes en una gráfica circular totalizan 100% y las

medidas angulares totalizan 360°.5. La suma de las medidas de los ángulos de un triángulo es 360°.6. Un triángulo se clasifica como obtusángulo si uno de sus

ángulos es obtuso.7. Todos los rectángulos son cuadriláteros, pero no todos los

cuadriláteros son rectángulos.8. Las figuras que son iguales en forma y tamaño se llaman

figuras semejantes.9. Si dos figuras son semejantes, entonces sus ángulos

correspondientes son congruentes.10. Un polígono es una figura bidimensional con cinco lados.11. Después de trasladar una figura, la figura resultante es igual

en tamaño y forma a la original.12. Sólo figuras con por lo menos un eje de simetría pueden

transformarse mediante reflexión.


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Lesson Reading GuideAngle Relationships

Get Ready for the LessonRead the introduction at the top of page 510 in your textbook. Writeyour answers below.

1. Name other times in which the hands of a clock form angles less than 90°, equal to 90°, and greater than 90°.

2. How many degrees is the angle that is formed by clock hands at 6:00?

Read the Lesson3. Give three possible names for the angle shown to the right.

4. Draw the correct angle under each heading.

Obtuse angle Acute angle

Right angle Straight angle

5. Fill in the blanks with the correct angle number.

� and � are vertical angles.

� and � are adjacent angles.

Remember What You Learned6. Work with a partner. Have your partner draw two angles. Identify the

types of angles your partner has drawn.

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Study Guide and InterventionAngle Relationships


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Classify each angle as acute, obtuse, right, or straight.

A. The angle is less B.than 90°, so it isan acute angle.

Label the two angles vertical or adjacent.

C. These angles are D.vertical because they are opposite each other and formed by two intersecting lines.


1. 2. 3. 4.

Label the angles vertical or adjacent.

5. 6. 7. 8.7

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• An angle has two sides that share a common endpoint. The point where the sides meet is called thevertex. Angles are measured in degrees, where 1 degree is one of 360 equal parts of a circle.

• Angles are classified according to their measure.

• Two angles are vertical if they are opposite angles formed by the intersection of two lines.

• Two angles are adjacent if they share a common vertex, a common side, and do not overlap.

Right Angle Acute Angle Obtuse Angle Straight Angle

Example 1

Example 2

Exercises

The angle is greaterthan 90°, so it is anobtuse angle.

These angles areadjacent because theyshare a common vertex,a common side, and donot overlap.

�1 and �3 are vertical angles.�4 and �2 are vertical angles.

�5 and �6 are adjacent angles

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Skills PracticeAngle Relationships


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1. 2. 3.

4. 5. 6.

7. 8. 9.

Estimate the measurement of each angle in degrees.

10. 11. 12.

Use the figure at the right to answer Questions 13–15.

13. Name the acute angles.

14. Name the obtuse angles.

15. Name two angles that are adjacent.

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Name each angle in four ways. Then classify the angle as acute, right,obtuse, or straight.

1. 2. 3.

4. 5. 6.

Use the figure at the right to answer Questions 7 and 8.

7. Name two angles that are vertical.

8. Name two angles that are adjacent.

Use the figure at the right to name the following.

9. two acute angles

10. two straight angles

11. two right angles

12. two obtuse angles

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PracticeAngle Relationships


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Word Problem PracticeAngle Relationships


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1. CLOCKS The time shown on the clock is 11:05. Starting at this time,approximately what time will it bewhen the hands form an obtuse angle?

2. AIRPORT The runways at a local airport are sketched in the figure.Classify �1 and �2 as acute, obtuse,right, or straight.

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3. FOUR SQUARE Lauren, James, Lisa,and Lauretta were playing four square.Which students are standing at vertical angles from one another?

Lauren James

Lisa Lauretta

4. CLOCKS The time shown on the clock is12:07. After 20 minutes have gone by,will the angle formed by the hour andminute hands be acute, obtuse, right,or straight?

5. BALLET When a ballet dancer’s feet arein first position, the heels are touching,and the feet are turned out. A dancerwith excellent technique can positionhis or her feet so that they are nearlyin a straight line. Isabella is practicingher technique. Classify the angle herfeet form as acute, obtuse, or right.

6. PARKING LOT Eric, Ryan, Aisha, and Abbey are all parked in the school lot.Who is parked at adjacent angles fromone another?

Aisha

RyanEric

Abbey

6MG2.1

Angles in BaseballAngles play an important part in many sports. In baseball, infieldersstand on and cover different parts of the infield depending on theposition of the runners. Sometimes, a player will have to turn varyingangles to make plays.

For Exercises 1 and 2, look at these pictures of baseball fields. In eachone, the four infielders cover different areas of the diamond. Use aprotractor to determine the measure of the angle of the area coveredby the 2nd baseman with different runner positions.

1. 2.

3. The outfield is covered by three other players:the left, center, and right outfielders. The areasthey cover may overlap slightly depending onwhoever is closest to the ball; but in general,each player has an area to cover. This figure shows the area most often covered by each outfielder. What type of angle does each area make with home plate? What type of angle do all three outfield areas combined create with home plate?

4. During a game, the pitcher notices the runner on second base wants to steal third base. If the pitcher is facing home plate, what type of angle does the pitcher have to turn through to throw the ball to third base?

5. During a different inning, a runner is on first base and appears to wantto steal second base. What type of angle does the pitcher need to turnthrough to throw the ball to second base if the pitcher is facing homeplate?

HomePlate

ThirdBase

SecondBase Area covered

by right fielder

Area coveredby center fielder

Area coveredby left fielder

FirstBase

HomePlate

ThirdBase

SecondBase Area covered by the

second baseman

FirstBase

HomePlate

ThirdBase

SecondBase Area covered by the

second baseman

FirstBase

NAME ________________________________________ DATE ______________ PERIOD _____

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NAME ________________________________________ DATE ______________ PERIOD _____


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Get Ready for the LessonComplete the Mini Lab at the top of page 514 in your textbook.Write your answers below.

1. Classify the angle as acute, right, obtuse, or straight.

2. Copy the angle onto a piece of paper. Then draw a ray that cuts the angle into two congruent angles. Label these two congruent angles �1 and �2.

3. What is m�1 and m�2?

4. What is the sum of m�1 and m�2?

5. Copy the original angle onto a piece of paper. Then draw a ray that separates the angle into two non-congruentangles. Label these two angles �3 and �4.

6. What is true about the sum of m�3 and m�4?

7. Complete Exercises 1–6 for the angle shown at the right.

Read the LessonFill in the blanks to answer Questions 8 and 9.

8. Two angles are complementary if the sum of their measure is .

9. Two angles are supplementary if the sum of their measure is .

Remember What You Learned10. 11.

45°x°35°

x°

6MG2.1, 6MG2.2Lesson Reading GuideComplementary and Supplementary Angles

NAME ________________________________________ DATE ______________ PERIOD _____


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10-2

Find the value of x.

The two angles form a right angle or 90°, so they are complementary,

Write the equation.Subtract 43 from each side.

so the value of x is 47°.


The two angles form a straight line or 180°, so they are supplementary,

Write the equation.Subtract 110 from each side.

so the value of x is 70°.

Find the value of x in each figure.

1. 2. 3.

4. 5. 6.

82° x°45°x°71°

x°

85°x°

56°

x°

58° x°

110 � x � 180� 110 � 110

x � 70110˚ x ˚

43 � x � 90� 43 � 43

x � 4743°

x°

• Two angles are complementary if the sum of their measure is 90°.

m�1 � m�2 � 90°

• Two angles are supplementary if the sum of their measure is 180°.

m�3 � m�4 � 180°

• To find a missing angle measure, first determine if the angles are complementary orsupplementary. Then write an equation and subtract to find the missing measure.

3 4

12

Example 1

Example 2

Exercises

6MG2.1, 6MG2.2Study Guide and InterventionComplementary and Supplementary Angles

NAME ________________________________________ DATE ______________ PERIOD _____


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Find the missing angle measure.

1. 2. 3.

4. 5. 6.

7. 8. 9.

Use the figure at the right to answer Questions 10–13.

10. Find m�HJL.

11. �HJL and �LJM are what type of angles?

12. Find m�KJM.

13. �KJL and �LJM are what type of angles?

K

JH M

L

90°30°

60°

24°

x°

43°

43° x°45° 65°

x°

10° x°

85° x°

42°

x°

25˚

x ˚42˚

x ˚127˚ x ˚

6MG2.1, 6MG2.2Skills PracticeComplementary and Supplementary Angles

NAME ________________________________________ DATE ______________ PERIOD _____


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10-2

Find the value of x in each figure.

1. 2. 3.

4. 5. 6.

Classify each pair of angles as complementary, supplementary, or neither.

7. 8. 9.

ALGEBRA Find the value of x in each figure.

10. 11. 12.

13. ALGEBRA If �C and �D are supplementary, and the measure of �Dis 45°, what is the measure of �C?

19.2˚ x˚

92˚ 78.5˚

x˚

49.1˚

x˚

12

12

1 2

72° x°110°

x°29°

x°

43°

x°65°x°22°

x°

6MG2.1, 6MG2.2PracticeComplementary and Supplementary Angles

NAME ________________________________________ DATE ______________ PERIOD _____


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1. SIGN The support wire for a sign meets the wall and the overhang asshown below. If m�2 � 42°, find m�1.Explain your reasoning

21

2. STREETS Main Street intersects Oak Road. If a right-hand turn ontoOak Road requires a 77° turn, whatdegree must a left-hand turn onto Oak Road make?

77˚

Oak Road

Main Street

3. RAILROAD East of the town of Rockport,the railroad tracks intersect Highway 67as shown below. If m�1 � 133°, find m�2. Explain your reasoning.

12

4. CAMPING Jonna and Elizabeth found alevel campsite and pitched their tent asshown below. If m�1 � 120°, find m�2.Explain your reasoning.

2 1

5. GAS GAUGE Below is a picture of the gas gauge in Sergio's car. Theangles made by the indicator arecomplementary. If the m�1 � 42°,what is the m�2?

FUEL

E F1 2

6. ARCHITECTURE The plans for a newaquarium call for several hallways ofexhibits leading out of a circular mainroom. Because of the size of the tanksthat will be used, the angle formedbetween two adjacent hallways can beno smaller than 65°. What is themaximum number of hallways that canbe built leading out of the main room?

Main Room Hallway

Hallway

65˚

6MG2.1, 6MG2.2Word Problem PracticeComplementary and Supplementary Angles

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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10-2

Matchstick PuzzlesThe puzzles on this page involve a box of wooden matches.Toothpicks or any other straight objects may be also be used.

Use the square figure at the right to make each of the followingfigures.

1. Move 3 matches to make 2. Move 4 matches to make3 identical squares. 3 identical squares.

3. Remove 2 matches to 4. Move 2 matches to makemake 2 squares. 7 squares. (You may cross

the matches in this one only.)

Use the hexagonal figure at the right to make each of the following firgures.

5. Move 4 matches to make 6. Move 4 matches to make3 equilateral triangles. 4 identical diamonds.

Use the square figure at the right to make each of the following firgures.

5. Remove 4 matches to 6. Remove 6 matches to makemake 5 identical squares. 5 identical squares.

6MG2.3

NAME ________________________________________ DATE ______________ PERIOD _____


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Get Ready for the LessonRead the introduction at the top of page 518 in your textbook.Write your answers below.

1. Explain how you know that each person surveyed chose only one shade ofblue.

2. If 500 people took part in the survey, how many preferred aquamarine?

Read the Lesson3. In the following circle graph, what is the percent represented by

section C? How do you know?

4. As stated in Example 2 on page 519, when you construct a circle graph,you can check your work by measuring the last section of a circle graph to verify that the angles have the correct measures. Why will this work as a check?

Remember What You Learned5. If you are given the results of a survey and the results are given in

percents, how do you draw a circle graph to represent the results of thesurvey? Describe each step.

Successful SpaceLaunches, 2001

12.5%B

C

25%A

5SDAP1.2Lesson Reading GuideStatistics: Display Data in a Circle Graph

NAME ________________________________________ DATE ______________ PERIOD _____


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10-3

Exercises

ENERGY Make a circlegraph of the data in thetable.

Step 1 Find the total number of reactors:104 � 59 � 54 � 222 � 439.

Step 2 Find the ratio that compares eachnumber with the total. Write theratio as a decimal rounded to the nearest hundredth.

United States: �140349�

� 0.24 Japan: �45349�

� 0.12

France: �45399�

� 0.13 Other: �242329�

� 0.51Step 3 Find the number of degrees for each section of the graph.

United States: 0.24 · 360� � 86� Japan: 0.12 · 360� � 43�

France: 0.13 · 360� � 47� Other: 0.51 · 360� � 184�

Step 4 Use a compass to construct a circle and draw a radius. Then use a protractor to draw an 86° angle. This represents the percent of nuclear reactors in the United States.

Step 5 From the new radius, draw a 47° angle forFrance. Repeat this step for the other twosections. Label each section and give the graph a title.

1. SWIMMING The table shows the number of members of the swim teamwho competed at the swim meet. Each competed in only one event. Makea circle graph of the data.

Nuclear Reactors in Operation, 2001

24%UnitedStates

51%Other

Countries

12%Japan

13%France

A graph that shows data as parts of a whole circle is called a circle graph. In a circle graph, the percents add up to 100. When percents are not given, you must first determine what part of the wholeeach item represents.

Swim Team Member Participation

Butterfly

Event Number

Freestyle 18

Breaststroke 7

Backstroke 5

2

Swim Team Member Participation

Example 1

Other Countries

United States 104

France 59

Japan 54

222

Country Number of Reactors

Nuclear Reactors in Operation, 2001

5SDAP1.2Study Guide and InterventionStatistics: Display Data in a Circle Graph

NAME ________________________________________ DATE ______________ PERIOD _____


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For each table, find the number of degrees in each section of a circlegraph. Then make a circle graph of the data.

1. 2.

3. 4.

United States CoastlineSuccessful Space Launches, 2001

Family Members Students Confide InUnited States Energy Usage, 2001

United States Energy Usage, 2001

Other

Category Percent

Commercial and Industrial 52%

Residential 20%

Transportation 27%

1%

Family Members Students Confide In

Grandparent/Other

Family Member Percent

Mom 52%

Dad 17%

Brother/Sister 16%

15%

Successful Space Launches, 2001

China

Country Number

India 2

United States 23

European Space Agency 7

1

United States Coastline

Coast Length (miles)

Atlantic 2,100

Pacific 7,600

Gulf 1,600

Arctic 1,100

United States Coastline

Arctic

Coast Length (mi)

Atlantic 2,100

Pacific 7,600

Gulf 1,600

1,100

5SDAP1.2Skills PracticeStatistics: Display Data in a Circle Graph

NAME ________________________________________ DATE ______________ PERIOD _____


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10-3

Display each set of data in a circle graph.

1. 2.

EXPORTS For Exercises 3 and 4, use the circle graph that shows the percent of Persian Gulfpetroleum exports by country for the year2003.

3. Which country has the most petroleum exports?

4. How many times more exports does Iran have than Qatar?

DATA SENSE For each graph, find the missing values.

5. 6. Time Management

Chores28˚

Other36˚ Sleep

130˚

Meals42˚

Hygiene24˚

Schoolx˚

Recycled Products

Aluminum25% Electronics

x%

Plastic20%

Other15%

Newspaper30%

Persian Gulf Exports 2003

SaudiArabia49%

Iraq5% Iran

15%

Kuwait12%

Qatar5%

United ArabEmirates14%

America’s Energy SourcesVolume of World’s Oceans

America’s Energy SourcesType Percent

Petroleum 40%Natural Gas 23%

Coal 22%Nuclear 8%Other 7%

Volume of World’s OceansOcean PercentPacific 49%

Atlantic 26%Indian 21%Arctic 4%

Source: conocophillips.com

Source: peacecorps.gov

5SDAP1.2PracticeStatistics: Display Data in a Circle Graph

NAME ________________________________________ DATE ______________ PERIOD _____


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LANGUAGES For Exercises 1 and 2,use the table that shows thenumber of people that speak thefive languages that are spokenby the most people in the world.

MILITARY For Exercises 3 and 4, use the table that shows the numberof people active in the United Statesmilitary in 2002.

CategoryCommercial and IndustrialResidentialTransportationOther

Spanish

Language Speakers (millions)

Hindi 366

English 341

322

Bengali 207

Chinese, Mandarin 874

Languages Spoken by the Most People

1. Find the degrees for each part of acircle graph that shows the data.

2. Make a circle graph of the data. Whichthree languages account for 41% of thetotal?

Languages Spoken by the Most People

Coast Guard

Air Force

Branch Personnel (thousands)

Navy 385

Marine Corps 174

368

38

Army 486

3. Make a circle graph of the data.United States Military Personnel Active Duty, 2002

4. Which two branches taken togetheraccount for almost half of the total?

United States Military, Active Duty, 2002

5SDAP1.2Word Problem PracticeStatistics: Display Data in a Circle Graph

NAME ________________________________________ DATE ______________ PERIOD _____


10-3 Enrichment

Relative Frequency and Circle GraphsThe relative frequency tells how the frequencyof one item compares to the total of all thefrequencies. Relative frequencies are written asfractions, decimals, or percents.

For example, in Exercise 1 below, the total of allthe frequencies is 50. So, the relative frequency ofthe grade A is 8 � 50, or 0.16.

The circle at the right is divided into 20 equalparts. You can trace this circle and then userelative frequencies to make circle graphs.

Complete each chart to show the relativefrequencies. Then sketch a circle graph forthe data. Use decimals rounded to the nearest hundredth.

1. History Grades for 50 Students

2. Steve’s Budget

D 6

C18Frequency

8

16

Grade

18

A

6

B

RelativeFrequency

C

D

0.16

2F

AmountSpent

$26

$46

Item

$24

Telephone

$38

Movies

RelativeSpending

Books

Car

$66Other

0 0.050.1

0.15

0.2

0.3

0.35

0.40.450.50.55

0.25

0.6

0.65

0.7

0.75

0.8

0.85

0.90.95

History Grades for 50 Students

Steve’s Budget

5SDAP1.2

NAME ________________________________________ DATE ______________ PERIOD _____

TI-73 ActivityCircle Graphs


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Use your calculator to make circle graphs from data.

A group of students took a survey of favorite soft drinks. Make a circle graph

and find the percent of each favorite soft drink. Here is theirdata table.

Step 1 Enter the data into lists. Enter the category data in L1and the number data in L2. Remember to use quotesaround the first item in the category data. You canabbreviate the category names.

[MEM] 6 Move right and highlight the first blank list.Name the category DRINK.

[TEXT] " D R I N K " Done

[TEXT] " C O L A " Done

Note: The letter c appears in L1, because it contains category data.Fill in the rest of the drink categories. Enter the number data in a list called NUMBER.

Step 2 Set Plot 1. First turn off all plots.

[PLOT] 4

[PLOT] 1

Make sure Drink is the CategList and Number is the Data List. Choose Number.

Step 3 Create the circle graph. Analyze the graph.

Use cursor keys with .

Step 4 Create a circle graph showing percents. Choose Percent on the Plot 1 screen.

[PLOT] 1

In the key shown beside the graph, read the percents for each soft drink.

Refer to circle graph you created.

1. Describe the circle graph.

2. Use the percent circle graph. List the percents for each soft drink.

3. What does the circle graph tell you about the favorite soft drinks of the studentssurveyed? Use percents in your description.

GRAPHENTER2nd

TRACEGRAPH

TRACE

ENTER

ENTERENTER2nd

ENTER2nd

ENTER2nd

ENTER2nd

LISTENTER2nd

Category Number of(Soft Drink) Students

cola 28

diet cola (DC) 9

root beer (RB) 26

lemon-lime (LL) 13

other 8

Example

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading Guide Triangles


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10-4

Get Ready for the LessonComplete the Mini Lab at the top of page 524 in your textbook. Writeyour answers below.

1. What kind of angle is formed where the three vertices meet?

2. Repeat the activity with another triangle. Make a conjecture about thesum of the measures of the angles of any triangle.

Read the Lesson3. How can you indicate that two sides of a triangle are congruent?

4. Write the following equation in words: m�1 � m�2 � m�3 � 180�.

5. If you know the measures of two angles of a triangle, how can you findthe measure of the third angle?

Remember What You Learned6. Complete the table to help you remember the ways to classify triangles.

Classified by Angles or Sides

angles

Type of Triangle

sides

acute

obtuse

Description

no congruent sides

1 right angle

isosceles

equilateral

6MG2.2, 6MG2.3

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionTriangles


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Find the value of x in �ABC.

x � 66 � 52 � 180 The sum of the measures is 180.x � 118 � 180 Simplify.

� 118 � 118 Subtract 118 from each side.x � 62

The missing angle is 62�.

Classify the triangle by its angles and by its sides.

The triangle has one obtuse angle and two sides the same length. So, it is an obtuse, isosceles triangle.

Find the missing measure in each triangle. Then classify the triangleas acute, right, or obtuse.

1. 2. 3.

Classify each triangle by its angles and by its sides.

4. 5. 6.

40˚

110˚ 30˚

60˚

70˚50˚

45˚

40˚ x˚43˚

x˚82˚

˚x75˚

Triangles can be classified by the measures of their angles. An acute triangle has three acute angles.An obtuse triangle has one obtuse angle. A right triangle has one right angle.

Triangles can also be classified by the lengths of their sides. Sides that are the same length arecongruent segments and are often marked by tick marks. In a scalene triangle, all sides havedifferent lengths. An isosceles triangle has at least two congruent sides. An equilateral triangle hasall three sides congruent.

A triangle is a figure with three sides and three angles. The symbol for triangle is �. The sum of the measures of the angles of a triangle is 180�.You can use this to find a missing angle measure in a triangle.

A

B

C

66˚

˚x52˚

120˚

Example 1

Example 2

6MG2.2, 6MG2.3

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeTriangles


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10-4

Find the missing measure in each triangle. Then classify the triangleas acute, right, or obtuse.

1. 2. 3.

4. 5. 6.

7. 8. 9.


10. 11. 12.

13. 14. 15.

16. 17. 18.

27˚46˚

82˚

52˚

98˚

121˚40˚

19˚60˚

60˚

60˚

50˚

40˚114˚

37˚

50˚x˚

126˚ 22˚

x˚51˚

57˚

x˚

71˚

45˚x˚

65˚

x˚38˚

38˚

x˚

49˚

x˚24˚

36˚

x˚

81˚84˚x˚

6MG2.2, 6MG2.3


1. 2. 3.

4. 5. 6.

Find the missing measure in each triangle with the given angle measures.

7. 45°, 35.8°, x° 8. 100°, x°, 40.7° 9. x°, 90°, 16.5°

10. Find the third angle of a right triangle if one of the angles measures 24°.

11. What is the third angle of a right triangle if one of the angles measures 51.1°?

12. ALGEBRA Find m�A in � ABC if m�B � 38° and m�C � 38°.

13. ALGEBRA In �XYZ, m�Z � 113° and m�X � 28°. What is m�Y?

Classify the marked triangle in each object by its angles and by its sides.

14. 15. 16.

ALGEBRA Find the value of x in each triangle.

20. 21. 22.

2x˚ x˚

x˚7x˚

3x˚

2x˚ 2x˚

x˚

30˚ 30˚40˚

50˚25˚

60˚

60˚̊

x˚

41˚

37˚x˚

29˚

61˚̊

x˚

17˚

x˚

22˚

140˚ x˚

42˚ x˚

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeTriangles


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeTriangles


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10-4

1. TAILORING Each lapel on a suit jacket isin the shape of a triangle. The threeangles of each triangle measure 47�,68�, and 65�. Classify the triangle by itsangles.

2. FLAGS A naval distress signal flag is inthe shape of a triangle. The three sidesof the triangle measure 5 feet, 9 feet,and 9 feet. Classify the triangle by itssides.

3. CARPENTRY The supports of a woodtable are in the shape of a righttriangle. Find the third angle of thetriangle if the measure of one of theangles is 23�.

4. MAPS The three towns of Ripon,Sparta, and Walker form a triangle asshown below. Classify the triangle byits angles and by its sides. What is thevalue of x in the triangle?

38˚

104˚ ˚x

Ripon

Sparta Walker

47 mi30 mi

30 mi

5. HIKING The figure shows the OakCreek trail, which is shaped like atriangle. Classify the triangle by itsangles and by its sides. What is thevalue of x in the figure?

61˚

78˚ ˚x

Rocky Peak

Meadow Trail Head

1.2 mi0.8 mi

1.1 mi

Oak Creek

6. LADDER The figure shows a ladderleaning against a wall, forming atriangle. Classify the triangle by itsangles and by its sides. What is thevalue of x in the figure?

66˚

˚x

9 ft

4 ft

6MG2.2, 6MG2.3

Triangle SumsThe measures of the angles of a triangle always add up to 180°. Thesides of a triangle also have a special relationship. In this activity,you will explore the relationships of the side lengths.Cut the strips of paper from the right side of this page. Use the 3specified strips for each problem. Tell if a triangle can be formedwith them. If so, tell what type of triangle it is.

1. 6 cm, 14 cm, and 14 cm 2. 6 cm, 6 cm, 14 cm

3. 6 cm, 8 cm, 14 cm 4. 3 cm, 3 cm, 6 cm

5. 3 cm, 6 cm, 8 cm 6. 6 cm, 6 cm, 8 cm

7. Look at your answers above. Choose any set of side lengths that form atriangle. Add the two shortest measures. Compare that sum with thelongest side length. Try this with all the triangles above. What conclusioncan you make about triangle side lengths?

8. Now look at the sets of side lengths that did not form triangles. Add thetwo shortest sides. Compare the sum with the length of the third side.What conclusion can you make about three lengths that do not make atriangle?

9. What rule can you give to test any three segment lengths to find out ifthe segments will form a triangle?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Example Use the formula d � rt where d is distance, r is rate, and t is time to determine how far a car has traveled after 4 hours if

it is traveling at a rate of 65 mph.

NAME ________________________________________ DATE ______________ PERIOD _____


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Logical reasoning is a method of problem solving that uses inductive reasoning, making a rule afterseeing several examples or deducting reasoning, use a rule to make a decision.

Explore You know the car has traveled for 4 hours at 65 mph.Plan Try a few examples to find a pattern. Make a table.

Solve

After each hour the car has traveled 65 more miles. So after 4 hours the carwill have traveled 260 miles.

Examine The formula is d � rt so d � 65 � 4 or 260 mi.

Hours Passed Distance Traveled(in miles)

1 651.5 97.52 130

2.5 162.53 195t 65t

Solve the following problems using logical reasoning.

1. TRAVEL Use the formula d � rt where d is the distance, r is the rate, andt is the time to determine how far the Moralez family has traveled if theyare driving at a rate of 72 miles per hour for 9 hours.

2. CELL PHONES Determine the cost per phone call if Maria made 30 callslast month and her total bill for the month was $45.00.

3. MUSIC Sarah, Juan, and Derrick play the piano, trumpet, and violin, butnot necessarily in that order. Sarah and Derrick sit on either side of thetrumpet player. Sarah does not play the violin. Who plays the violin?

Exercises

6MR1.2, 6MG2.3Study Guide and InterventionProblem-Solving Investigation: Use Logical Reasoning

Use logical reasoning to solve.

1. GEOMETRY Draw several squares and measure their interior angles. Whatcan you conclude about the measures of the angles of a square? Did youuse inductive or deductive reasoning?

2. MONEY Luke is investing money in a savings account. Use the formula I � Prt where I is the amount of interest earned, P is the principalamount of money invested, r is the interest rate, and t is the length oftime the money is invested. If Luke invests 500 at 5% interest for 1 year,how much interest will he earn? Did you use inductive or deductivereasoning?

3. PATTERNS Write a rule to represent the pattern shown below. Did you useinductive or deductive reasoning? 2, 4, 6, 8, 10, …

4. STUDENT COUNCIL Chen, Sue and Jacob are president, vice president andsecretary of the student council, not necessarily in that order. Chen andthe vice president stayed after school with Jacob to plan a dance. Chen isnot the president. Who is the president?

5. GEOMETRY Draw several parallelograms and measure their sides. Whatcan you conclude about the measures of the opposite sides of aparallelogram? Did you use inductive or deductive reasoning?

6. TRAVEL Use the formula D � rt where D is the distance, r is the rate, andt is the time to determine how far Lucinda traveled if she drove 65 milesper hour for 6 hours without stopping. Did you use inductive or deductivereasoning?

NAME ________________________________________ DATE ______________ PERIOD _____


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c.10-5 6MR1.2, 6MG2.3Skills Practice

Problem-Solving Investigation: Use Logical Reasoning

Select the Operation

Mixed Problem Solving

For Exercises 1 and 2, use logicalreasoning to solve the problem.

1. TOWNS Tia, Bianca, and Hiroko live inthe towns of Parkside, Westlake, andSummerville, but not necessarily in thatorder. Tia and her friend that lives inWestlake helped Bianca with her chores.Bianca does not live in Parkside. Wheredoes Tia live? Did you use inductive ordeductive reasoning?

2. GEOMETRY Draw a right triangle. Markthe midpoints of each side of thetriangle and draw a smaller triangle byconnecting the midpoints. Do thisseveral more times. What can youconclude about the smaller triangle? Did you use inductive or deductivereasoning?

Use any strategy to solve Exercises 3and 4. Some strategies are shown below.

3. ANGLES One angle of a triangle is 33°less than the other two angles. Find themeasures of the angles of the triangle.Did you use inductive or deductivereasoning?

4. METEORITES An astronomer found threemeteorites weighing 9.4 pounds, 5.7pounds, and 24.5 pounds. If 1 kilogramweighs 2.2 pounds, find the averagemass of the meteorites in kilograms.

For Exercises 5 and 6, select theappropriate operation(s) to solve theproblems. Justify your selections andsolve the problem.

5. PUBLIC TRANSPORTATION A bus stoppedat a bus stop and 12 people got on and 5 got off. At the next stop, 14 people goton and 3 got off. If the number ofpassengers has doubled, find thenumber of passengers on the bus.

6. DISCOUNTS The table shows thedifferent discounts two stores offer forthe same product. Which store offers thebetter price after the discount is appliedand by how much?

NAME ________________________________________ DATE ______________ PERIOD _____


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PROBLEM-SOLVING STRATEGIES

• Use the four-step plan.

• Look for a pattern.

• Use a graph.

• Use logical reasoning.

Price DiscountStore A $129.00 $25Store B $139.00 25%

6MR1.2, 6MG2.3PracticeProblem-Solving Investigation: Use Logical Reasoning

NAME ________________________________________ DATE ______________ PERIOD _____


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1. PHYSICS A ball is dropped from a heightof 40 feet. If the ball bounces �

12

� as highon each successive bounce, what is theheight on the fourth bounce?

2. RECIPES Shawn is making a cake. Heneeds a total of 3�

14

� cups of flour. If hehas already added 2�

12

� cups, how muchmore does he need to add?A 2 cups C �

12

� cup

B 1 cup D �34

� cup

3. GEOMETRY Draw several pentagonsand measure their interior angles.What can you conclude about the sumof the measures of the angles of apentagon? Did you use inductive ordeductive reasoning?

4. PATTERNS Find the next three terms is the sequence.2, 5, 9, 14, …

5. WORK The table below shows howmuch Lu got paid based on the numberof hours she babysat. Predict her payfor 7 hours.

6. GEOMETRY Use the formula V � Bhwhere V is the volume of a cylinder,B is the area of the base and h is theheight of the cylinder to find thevolume of the cylinder below.

B = 3.5 in2

h = 8 in

7. FRAMING A photograph is 8 in. by 10 in. and is to be surrounded by a matthat is 1.5 in. all around. What will bethe dimensions of the picture and mattogether?

8. SCHOOL Students filled out a surveyabout their favorite school subjects. Theresults are shown in the bar graphbelow. How many more students listedEnglish as their favorite subject thanmath?

SocialStudies

Math English Science

20

10

0

3025

15

5

Number of hours Pay1 $52 $103 $154 $20

6MR1.2, 6MG2.3Word Problem PracticeProblem-Solving Investigation: Use Logical Reasoning

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading Guide Quadrilaterals


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Get Ready for the LessonRead the introduction at the top of page 533 in your textbook.Write your answers below.

1. Describe the angles inside the four-sided figure.

2. Which sides of the figure appear to be parallel?

3. Which sides appear to be congruent?

Read the Lesson4. In the diagram of quadrilaterals on page 533, what do the arrowheads on

the parallelogram and trapezoid indicate?

5. Why are all the figures on the page called quadrilaterals?

6. How is a trapezoid different from a rhombus, a square, and a rectangle?

7. In the diagrams of the parallelogram, rhombus, square, and rectangle,how do you know that certain sides are congruent?

Remember What You Learned8. Work with a partner. Take turns drawing quadrilaterals. Have the other

person give all possible names for the quadrilateral. Then decide on thebest name for the quadrilateral. For example, if one person draws asquare, the other person should say that it is a quadrilateral, aparallelogram, a rectangle, and a rhombus, but the best name for thefigure is a square.

6MG2.3

Example

Exercises

Quadrilaterals can be classified using their angles and sides. The best description of a quadrilateral isthe one that is the most specific.

Examples

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionQuadrilaterals


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Classify the quadrilateral using the name that best describes it.

a The quadrilateral is a parallelogram with 4 congruent sides. It is a rhombus.

b The quadrilateral has one pair of parallel sides.It is a trapezoid.

c The quadrilateral is a parallelogram with 4 right angles.It is a rectangle.

Find the missing measure in the quadrilateral.

100 � 110 � 60 � x � 360 Write the equation.270 � x � 360 Simplify.

� 270 � 270 Subtract 270 from x � 90 each side.

So, the missing measure is 90°.


1. 2. 3.

Find the missing angle measure in each quadrilateral.

4. 5. 6.

125˚

54˚

96˚x˚95˚

72˚

82˚

x˚135˚

88˚45˚

x˚

100˚

110˚

60˚

x˚

Rectangle

parallelogram with4 right angles

Trapezoid

one pair of parallelsides

Rhombus

parallelogram with4 congruent sides

Square

parallelogram with4 right angles and4 congruent sides

Parallelogram

opposite sides parallel and

opposite sides congruent

6MG2.3

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeQuadrilaterals


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10-6


1. 2. 3.

4. 5. 6.

7. 8. 9.

Find the missing angle measure of each quadrilateral.

10. 11. 12.

13. 14. 15.

64˚

x˚

77˚

99˚ 109˚

x˚

72˚

121˚

x˚

89˚

92˚ 64˚

x˚135˚110˚

75˚x˚

52˚

x˚

6MG2.3

Classify each quadrilateral using the name that best describes it.

1. 2. 3.

4. 5. 6.

ALGEBRA Find the missing angle measure in each quadrilateral.

7. 8. 9.

10. 11. 12.

Find the missing measure in each quadrilateral with the given anglemeasures.

13. 63.2°, 56°, 111.7°, x° 14. 31.7°, x°, 161.3°, 51.4°

15. x°, 122.4°, 53.7°, 90° 16. 83.7°, 137.2°, x°, 28.5°

17. ALGEBRA Find m�C in quadrilateral ABCD if m�A � 110°, m�B � 88°,and m�D � 55°.

18. ALGEBRA What is m�Z in quadrilateral WXYZ if m�W � 86°, m�X � 88°,and m�Y � 92°?

ALGEBRA Find the value of x in each quadrilateral.

19. 20. 21.3x˚ 3x˚

3x˚ 3x˚

60˚

60˚ x˚

x˚68˚ 65˚

x˚ x˚

152˚

x˚120˚

110˚60˚

x˚

125˚

x˚

130˚ 50˚̊

50˚̊ x˚126˚78˚̊

54˚̊

x˚

107˚96˚̊

80˚̊

x˚

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeQuadrilaterals


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeQuadrilaterals


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10-6

1. KITES A kite is shown below. What isthe best name to classify the shape ofthe kite? Explain.

2. MAPS A map showing the roadconnecting the towns of Pike, Hudson,Placid, and Alton is shown. The roadconnecting Pike and Hudson is parallelto the road connecting Alton andPlacid. What is the best name toclassify the shape of the roadsconnecting the four towns? Explain.

HudsonPike

PlacidAlton

N

3. ART A picture frame is shown below.What is the best name to classify theshape of the frame?

1 ft

1 ft

4. SCHOOL SUPPLIES The side view of aneraser is shown below. What is the bestname to classify the shape of theeraser?

5. PARTY The front of a birthday partyinvitation is shown below. Find themeasure of the missing angle.

60˚ 120˚

120˚ x˚PARTY!

6. TABLE The top of Mr. Bautista’s newcoffee table is shown below. Find themeasure of the missing angle.

60˚

120˚ 100˚

x˚

6MG2.3

NAME ________________________________________ DATE ______________ PERIOD _____

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The Colormatch SquareTo work this puzzle, cut out the 16 tiles at the bottom of this page. The goal ofthe puzzle is to create a square so that the sides of any pair of adjacent tilesmatch. You are not allowed to rotate any of the tiles.

1. Complete the solution to the colormatch square puzzle below.

2. Find at least one other solution in which the A tile is in the upper leftcorner.

A D

PN

B G

L O

H

M

C

I KJ

FE

A

D

Whitesquaresmatch.

P

N

B

L

O

M

I

K

J

E

6MG2.3

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading Guide Similar Figures


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10-7

Get Ready for the LessonComplete the Mini Lab in your textbook. Write your answers below.

1. A�B� on the smaller rectangle matches E�F� on the larger rectangle.Name all pairs of matching sides in each pair of figures.

2. Write each ratio in simplest form.

a. �AE

BF�; �

FB

GC�; �

HD

GC�; �

EA

HD� b. �

RXY

S�; �

SY

TZ�; �

RXZ

T�

3. What do you notice about the ratios of matching sides.

4. Name all pairs of matching angles in the figures above. What do younotice about the measure of these angles?

5. MAKE A CONJECTURE about figures that have the same shape but not necessarily the same size.

Read the Lesson6. Write the statement �ABC � �DEF in words.

7. Write the statement �A � �D in words.

8. Suppose you know that two figures are similar, and that the followingcorresponding sides are proportional: side JK corresponds to side DE, andside KL corresponds to side EF. How would you write a proportion to findthe length of side KL if the lengths of all other sides are known?

Remember What You Learned9. Think of a real-life example that you could measure using indirect

measurement if you were given a miniature replica of your example.Explain how you could find an unknown measurement using known measurements of your example and the measurements of the replica.

6NS1.3

Exercises

Example 1

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionSimilar Figures


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If MNOP � RSTU, find the length of S�T�.

Since the two figures are similar, the ratios of their correspondingsides are equal. You can write and solve a proportion to find S�T�.

�UPO

T��

NST

O� Write a proportion.

�278�

� �n5

� Let n represent the length of ST. Then substitute.

7n � 28(5) Find the cross products.

7n � 140 Simplify.

n � 20 Divide each side by 7.

The length of S�T� is 20 feet.

Find the value of x in each pair of similar figures.

1. 2.

3. 4.

6 in.

5 in.

18 in.

B C

DA

F G

HE

x

9 yd

5 yd10 yd M N

OP

R S

TU

x

2 ft

4 ft

I

G

K

H

L

J

x

12 ft

3 m

5 m

A

B

F

C

D

E x

9 m

Figures that have the same shape but not necessarily the same size are similar figures. The symbol � means is similar to. You can use proportions to find the missing length of a side in a pair of similar figures.

For example �ABC � �DEF.Corresponding angles Corresponding sides

� A � � D �150� � �

48

� � �36

�

� B � � E

� C � � F

7 ft

5 ft

28 ft

M N

OP

R S

TU

4

3A

B

FC D

E

810

6

5

6NS1.3

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeSimilar Figures


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1. 2.

3. 4.

5. 6.

Determine whether each pair of figures is similar. Justify youranswer.

7. 8.

24 m

40 m15 m

8 m

D

F

EA

C

B

7 cm

9 cm

14 cm

18 cm

15 in.

12 in.

20 in.

B C

DA

E F

GH

x

6 mm

4 mm

M

OQ N

P

R x

9 mm

10 cm

7 cm

21 cm

B C

DA

F G

HEx

12 ft

14 ftA

B

E

C F G

x

18 ft

H

D

7 m3 m

N

M

R

O

Q

P

x9 m4 ft

3 ft

A

B

F

C

D

E x

6 ft

6NS1.3

1. Which rectangle is similar to rectangle RSTU?

2. Which triangle is similar to triangle XYZ?


3. 4.

5. 6.

7. FLAGPOLES Tasha wants to find the height ofthe flagpole at school. One morning, shedetermines the flagpole casts a shadow of 12 feet. If Tasha is 5 feet tall and casts a shadow of 3 feet, what is the height of theflagpole?

12 ft

x ft

3 ft

5 ft

4.2 mm1.5 mm

12.6 mm

x mm15 in.

8 in.24 in.

x in.

2 ft5 ft

7 ft

x ft 6 cm12 cm

12 cm

x cm

X

YZ

30 24 PR

T10 14

C

F

HGB

A32 3526 28

R S

TU

3

5

A B

CD

5

5

E FM N

Q PGH

6 8

10 2

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeSimilar Figures


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeSimilar Figures


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10-7

MODEL CARS For Exercises 1 and 2, use the following information. A scale model racing car is 11 inches long,3 inches wide, and 2 inches tall. The actual racing car is shown at the right.

PHOTOGRAPHY For Exercises 3–4, use the given information. James wants to enlarge a photograph that is 6 inches wide and 4 inches tall so that it fits into the frame shown.

30 in.

22 ft

1. How wide is the actual racing car? 2. How tall is the actual racing car?

3. How tall must the frame be for thepicture to fit?

4. Suppose James cuts 1 inch from the width of the photo, so that it is 5 inches wide, before he makes theenlargement. How tall will the framehave to be for the picture to fit?

5. MAPS A map below shows the towns ofDover, Butler, and Lodi. If the actualdistance between Dover and Butler is24 miles, how far is it from Dover toLodi?

Lodi

ButlerDover

4 in.

3 in.

6. BLUEPRINTS A blueprint for a house isshown below. If the front of the houseis actually 30 feet wide, how tall is thehouse?

12 in.

14 in.

6NS1.3

NAME ________________________________________ DATE ______________ PERIOD _____

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Similar Figures and AreasThe areas of two similar figures are related in a special way. Suppose that rectangle A is 2 units by3 units and rectangle B is 4 units by 6 units.

The area of rectangle A is 2 � 3 � 6 units2.

The area of rectangle B is 4 � 6 � 24 units2.

The lengths of the sides of rectangle B are twice those of rectangle A and the area of rectangle B is four times that of rectangle A.

Sketch figure B similar to figure A and satisfying the given condition.

1. Rectangle B has sixteen times the area of rectangle A.

2. Square B has an area that is 4 times that of square A.

3. Circle B has an area four times that of circle A.

Circle BCircle A

1.5

Square BSquare A

2

2

Rectangle BRectangle A

31

Rectangle BRectangle A

36

42

6NS1.3

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuidePolygons and Tessellations


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10-8

Get Ready for the LessonRead the introduction at the top of page 546 in your textbook. Writeyour answers below.

1. Find the difference between the shapes of the states in Group 1 and theshapes of the states in Group 2.

2. Why do most states have boundaries that are not straight line segments?

Read the Lesson3. How many straight lines can a polygon have?

4. What is a simple figure?

5. When you draw a figure, how can you tell whether or not it is closed?

6. How do you find the sum of the angle measures in a regular polygon?

7. In this lesson, the terms vertex and vertices are used. How are the termsrelated?

Remember What You Learned8. Using dot paper, draw a tessellation different from the ones shown in this

lesson. You can use all the same shape or you can use combinations ofshapes that form patterns. Share your work with your class.

6MR2.2 , 6AF3.2

Examples

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionPolygons and Tessellations


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Determine whether each figure is a polygon. If it is, classify thepolygon and state whether it is regular. If it is not a polygon,explain why.

The figure has 5 congruent sides The figure is not a polygonand 5 congruent angles. It is a because it has sides that overlap.regular pentagon.

Determine whether each figure is a polygon. If it is, classify thepolygon and state whether it is regular. If it is not a polygon, explainwhy.

1. 2. 3.

4. 5. 6.

120˚

A polygon is a simple, closed figure formed by three or more straight lines. A simple figure does nothave lines that cross each other. You have drawn a closed figure when your pencil ends up where itstarted. Polygons can be classified by the number of sides they have.

A polygon that has all sides congruent and all angles congruent is called a regular polygon.

decagon10 sides

nonagon9 sides

octagon8 sides

heptagon7 sides

hexagon6 sides

pentagon5 sides

6MR2.2 , 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticePolygons and Tessellations


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10-8

Determine whether each figure is a polygon. If it is, classify the polygonand state whether it is regular. If it is not a polygon, explain why.

1. 2. 3.

4. 5. 6.

7. 8. 9.

Find the measure of an angle in each polygon.

10. regular 15-gon 11. regular 18-gon 12. regular 24-gon

Classify the polygons that are used to create each tessellation.

13. 14.

15. What is the perimeter of a regular pentagon with sides 8.4 inches long?

6MR2.2 , 6AF3.2

Determine whether each figure is a polygon. If it is, classify the polygonand state whether it is regular. If it is not a polygon, explain why.

1. 2. 3.

4. 5. 6.

Find the measure of an angle in each polygon if the polygon is regular. Round tothe nearest tenth of a degree if necessary.

7. dodecagon 8. 14-gon 9. 18-gon 10. 36-gon(12-sided)

Classify the polygons that are used to create each tessellation.

11. 12.

13. What is the perimeter of a regular decagon with sides 6.2 meters long?

14. Find the perimeter of a regular hexagon having sides 5�23

� inches long.

KITES For Exercises 15–17, use the following information. A kite manufacturer makes kites in the shape of the figure shown.

15. Classify the shape of the kite.

16. If �K � �T and �E � 30°, find m�K and m�T.

17. Can a tessellation be made by using the shape of the kite? Justify your answer.

K T

I

E

NAME ________________________________________ DATE ______________ PERIOD _____

PracticePolygons and Tessellations


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticePolygons and Tessellations


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10-8

1. ROYALTY The outline of a crown wornby a king is shown below. Is the figurea polygon? If it is, classify the polygonand state whether it is regular. If it isnot a polygon, explain why.

2. ALCHEMY The symbol shown is one of the signs for salt alkali used in 17th-century chemistry. Is the symbol a polygon? If it is, classify the polygonand state whether it is regular. If it isnot a polygon, explain why.

3. JEWELRY The symbol shown is oftenused to represent gems. Is the symbol apolygon? If it is, classify the polygonand state whether it is regular. If it isnot a polygon, explain why.

4. SYMBOLS The 5-pointed star shown hassides of equal length. Is the symbol apolygon? If it is, classify the polygonand state whether it is regular. If it isnot a polygon, explain why.

5. STAIRS The figure shows a side view ofa set of stairs. Is the figure a polygon?If it is, classify the polygon and statewhether it is regular. If it is not apolygon, explain why.

6. TESSELLATIONS Identify the polygonsthat are used to create the tessellationshown in the figure.

6MR2.2 , 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Tessellated Patterns for Solid ShapesTessellations made from equilateral triangles can be used to buildthree-dimensional shapes. In Exercise 1, you should get a shape likethe one shown at the right. It is called a pyramid.

Copy each pattern. Crease the pattern along the lines.Then follow directions for folding the pattern. Use tape to secure the folded parts. When you have finished each model,describe it in words.

1. Fold 5 over 1.Repeat, in this order:

fold 6 over 7,fold 2 over 6.

2. Cut between 4 and 5. Then fold 5 over 3.Repeat in this order:

fold 6 over 5,fold 7 over 12, andfold 2 over 9.

3. Cut between 1 and 2 and between 14 and 15. Then fold 15 over 14.Repeat, in this order:

fold 1 over 2,fold 4 over 3,fold 11 over 1,fold 16 over 5, andfold 12 over 13.

1

5 710

14

69 11

12 13 15

16

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3 4

3

8 107 9

12

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5 6

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6MR2.2 , 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

TI-73 ActivityInterior Angles


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10-8

Use your calculator to explore interior angles of polygons. The sum of the measures of theinterior angles of a polygon with n sides is: Sum � (n � 2) � 180°.

If the polygon is regular, then the measure of each interior is this Sum divided by n, or �Sunm�.

Use and these formulas to complete the table below.

Step 1 Clear all lists. [MEM] 6

Step 2 Open the List feature.

Step 3 In L1, enter n, the number of sides.

Press after each value.

Step 4 In L2, enter the Sum of Interior Angles formula.

Highlight L2.

[TEXT] " Done [STAT] 1 2 180

[TEXT] " Done

Step 5 Highlight L3 and enter the formula for the measure of each angle.

[TEXT] " Done [STAT] 2 [STAT] 1

[TEXT] " Done 1. Check that the angle

measures for the octagon are correct by evaluating the expressions when n � 8.Do your calculations match the list values?

2. Describe the trends you see in the sum and the angle measure columns.

ENTERENTER

2nd2nd2nd2nd

ENTERENTER2nd

)2nd(2nd

ENTER

LIST

ENTER2nd

LIST

Name of Polygon Each Angle(Regular Polygon)

3 triangle 180° 60°

4

5

6

7

8

9

10

No. of Sides

Sum of InteriorAngles

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideTranslations


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1. Trace the horizontal and vertical path between corresponding vertices.What do you notice?

2. Add 5 to each x-coordinate of the vertices of the original figure. Thensubtract 2 from each y-coordinate of the vertices of the original figure.What do you notice?

Read the Lesson3. When translating a figure, what do you know about every point of the

original figure?

4. Can a figure be turned in a translation? Explain.

5. What notation is used to indicate the vertices of a translated figure?

6. Which figure is a translation of Figure 1—Figure 2 or Figure 3? Explain why one figure is a translation and why the other figure is not a translation.

Remember What You Learned7. Describe the translation given by the ordered pair (�7, 3). Think of a way

to remember which direction to translate when the x-coordinate of theordered pair describing the translation is negative.

1

2

3

7MG3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionTranslations


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10-9

Triangle ABC has vertices A(�4, �2), B(�2, 0), and C(�1, �3).Find the vertices of triangle ABC after a translation of 5 unitsright and 2 units up.

Add 5 to each x-coordinate. Add 2 to each y-coordinate.

The coordinates of the vertices of �ABC are A(1, 0), B(3, 2), and C(4, �1).

1. Translate �GHI 1 unit left and 2. Translate rectangle LMNO 4 units right5 units down. and 3 units up.

Triangle RST has vertices R(3, 2), S(4, �2), and T(1, �1). Find thevertices of RST after each translation. Then graph the figure andits translated image.

3. 5 units left, 1 unit up 4. 3 units left, 2 units downy

xO

T

R

S

y

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R

S

y

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O N

L M

y

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H

IG

A translation is the movement of a geometric figure in some direction without turning the figure. Whentranslating a figure, every point of the original figure is moved the same distance and in the samedirection. To graph a translation of a figure, move each vertex of the figure in the given direction. Thenconnect the new vertices.

y

xO

B'

C'

A'

A

B

C

Vertices of �ABCVertices of �ABC (x � 5, y � 2)

A(�4, �2) (�4 � 5, �2 � 2)

B(�2, 0) (�2 � 5, 0 � 2)

C(�1, �3) (�1 � 5, �3 � 2)

A(1, 0)

B(3, 2)

C(4, �1)

Example

Exercises

7MG3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeTranslations


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1. Translate �ABC 5 units left. 2. Translate rectangle RSTU 2 units rightand 5 units up.

3. Translate �DEF 4 units left and 4. Translate trapezoid LMNO 5 units right4 units down. and 3 units down.

Triangle XYZ has vertices X(�4, 5), Y(�1, 3), and Z(�2, 0). Find thevertices of XYZ after each translation. Then graph the figure andits translated image.

5. 5 units down 6. 4 units right, 3 units down

Parallelogram RSTU has vertices R(�1, �3), S(0, �1), T(4, �1), andU(3, �3). Find the vertices of RSTU after each translation. Thengraph the figure and its translated image.

7. 3 units left, 3 units up 8. 1 unit right, 5 units upy

xO

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y

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y

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y

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N

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C

7MG3.2

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeTranslations


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10-9

1. Translate rectangle ABCD 3 units right 2. Triangle PQR is translated 3 and 4 units down. Graph rectangle units left and 3 units down.ABCD. Then the translated figure is

translated 6 units right.Graph the resulting triangle.

Triangle EFG has vertices E(1, 1), F(4, � 3), and G(�2, 0). Find thevertices of E�F�G� after each translation. Then graph the figureand its translated image.

3. 3 units left, 2 units down 4. 4 units up

5. SEATS Jatin was given a new seating assignmentin science class. The diagram shows his old seat and his new seat. Describe this translation in words and as an ordered pair.

REASONING The coordinates of a point and its image after atranslation are given. Describe the translation in words and as anordered pair.

6. A(1, �2) → A (3, 4) 7. H(3, 3) → H (�4, 0) 8. Z(�2, �4) → Z(1, �5)

Front of Classroom

OLD

NEW

y

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y

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P

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7MG3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeTranslations


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MAPS For Exercises 1–4, use the map at the right. Maple St.

Blonde St.

Dodge St.

Pacific Ave.

Center Rd.

Harrison St.

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N

1. Stanley’s school is located at the cornerof Center and Elmwood. The library islocated at the corner of Dodge andDelaware. Describe Stanley’s walk fromschool to the library as an ordered pairof the number of blocks.

2. After he goes to the library, Stanleygoes to his Aunt Jeanne’s house at thecorner of California and Harrison.Describe Stanley’s walk from thelibrary to his aunt’s house as anordered pair of the number of blocks.

3. If a bus picks up passengers at thecorner of New York and Maple anddrives 2 blocks south and 3 blocks west, where does the bus end up?

4. Organizers of a walkathon want to mapout a route that will lead people fromthe corner of Center and Kensington tothe corner of California and Maple.Write a coordinate pair that describesthe most direct route.

5. GEOMETRY The figure shows anoctagon plotted on a coordinate system.The figure is to be translated by 5 unitsleft and 5 units down. Graph thetranslated image of the figure.

y

xO

6. BANKS Clarissa is waiting in line at the bank. There are several people inline in front of her. Describe the pathClarissa must take to get to the front of the line if each time she moves up in line by one position is considered one unit.

tellers

Clarissa

7MG3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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10-9

Chess MovesIn the game of chess, a knight can move several different ways. It can move twospaces vertically or horizontally, then onespace at a 90� angle. It can also move onespace vertically or horizontally, then twospaces at a 90� angle. Several examples of a knight’s moves are indicated on thegrid at the right.

1. Use the diagram at the right. Place a knight or other piece in the square marked 1. Move the knight so that it lands on each of the remaining white squares only once. Mark eachsquare in which the knight lands with 2, then 3, and so on.

2. Use the diagram below. Place a knight or other piece in the squaremarked 1. Move the knight so that it lands on each of the remainingsquares only once. Mark each square in which the knight lands with 2, then 3, and so on.

1

1

7MG3.2

Example

NAME ________________________________________ DATE ______________ PERIOD _____

Spreadsheet ActivityTranslations


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You can use a spreadsheet to determine and graph the ordered pairs of a figure after atranslation.

Quadrilateral ABCD has the vertices A(2, 3), B(�1, 2), C(�2, �3),and D(3, �1). Use a spreadsheet to find the vertices of quadrilateral

A'B'C'D' after a translation 4 units left and 2 units up. Then use the spreadsheet to create a graph of ABCD and A'B'C'D'.

Step 1 Use Column A for the x-coordinates and Column B for the y-coordinates. Enter thenumbers using the formula bar. Then press ENTER to move to the next cell. Be sure toenter the coordinates of the first point again at the end of the list.

Step 2 In cell C1, enter an equals sign followed by �A1�4. Then press ENTER to return the x-coordinate of the new point.

Step 3 In cell D1, enter an equals sign followed by �B1�2. Then press ENTER to return the y-coordinate of the new point.

Step 4 To find the remaining new x-coordinates, click on the bottom right corner of cell C1 anddrag it to cell C5. Click on the bottom right corner of cell D1 and drag it to cell D5 to findthe y-coordinates.

The coordinates of A'B'C'D' are A'(�2, 5), B'(�5, 4), C'(�6, �1), and D'(�1, 1).

Step 5 To graph, highlight columns A and B through row 5. Press the Chart Wizard. Select XY(Scatter) and choose the graph with data points connected by lines. Press NEXT. Selectthe SERIES tab. Press the ADD button. In the X-Values bar, enter �Sheet1!$C$1:$C$5. Inthe Y-Values bar, enter �Sheet1!$D$1:$D$5. Press NEXT, NEXT, FINISH to display the graph.

Quadrilateral QUAD hasvertices Q(�2, 1), U(2, 4),A(3, �3) and D(�1, �1). Usea spreadsheet to find thevertices of Q'U'A'D' after atranslation of 2 units rightand 3 units down. Then use aspreadsheet to graph QUADand Q'U'A'D'.

A B C D E F G H123456789

10111213141516

2-1-23

32

-3-1

-2-5-5-1

54

-11

2 3 -1 5

Sheet 1 Sheet 2 Sheet 3

-8 -6 -4 -2 2 4Series 1Series 2

-4-3-2-10123456

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideReflections


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10-10


1. Describe how you drew the reflection of your classmate’s name.

2. Explain why the line where the geomirror and paper meet is called theline of symmetry.

Read the Lesson3. Is the image of a reflection smaller, larger, or the same size as the

original figure?

4. In Example 4 on page 559, how can you tell that one image is a reflectionof the other across the x-axis?

5. Study the coordinates given in Examples 4 and 5 on page 559. How canyou tell how many units a vertex is away from the x-axis withoutgraphing it? How can you tell how many units a vertex is away from they-axis?

Remember What You Learned6. Work with a partner. Draw and cut out figures of regular polygons.

Demonstrate which regular polygons have lines of symmetry and whichdo not. Mark the lines of symmetry with dashed lines on the models.

7MG3.2

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionReflections


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Determine whether each figure has line symmetry. If so, draw alllines of symmetry.

no symmetry

Triangle DEF has vertices D(2, 2), E(5, 4), and F(1, 5). Find the coordinates of the reflected

image. Graph the figure and its reflected image over the x-axis.

Plot the vertices and connect to form �DEF. The x-axis is the line of symmetry. The distance from a point on �DEF to the line of symmetry is the same as the distance from the line of symmetry to the reflected image. The image coordinates are D(2, �2),E(5, �4), and F(1, �5).

For Exercises 1 and 2, determine which figures have line symmetry.Write yes or no. If yes, draw all lines of symmetry.

1. 2.

3. Triangle ABC has vertices A(0, 4), B(2, 1), and C(4, 3). Find thecoordinates of the vertices of ABC after a reflection over the x-axis. Then graph the figure and its reflected image.

y

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E'

D'

D

F'

F E

A type of transformation where a figure is flipped over a line of symmetry is a reflection. To draw thereflection of a polygon, find the distance from each vertex of the polygon to the line of symmetry. Plotthe new vertices the same distance from the line of symmetry but on the other side of the line. Thenconnect the new vertices to complete the reflected image.

Figures that match exactly when folded in half have line symmetry. Each fold line is called a line ofsymmetry. Some figures have more than one line of symmetry.

y

xO

Examples

Example 3

7MG3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeReflections


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10-10

Determine which figures have line symmetry. Then draw all lines ofsymmetry.

1. 2. 3.

4. 5. 6.

Graph the figure and its reflection over the x-axis. Then find thecoordinates of the reflected image.

7. triangle ABC with vertices A(�3, 4),B(1, 4), and C(3, 1)

8. rectangle MNOP with vertices M(�2, �4),N(�2, �1), O(3, �1), andP(3, �4)

Graph the figure and its reflection over the y-axis. Then find thecoordinates of the reflected image.

9. triangle DEF with vertices D(1, 4), 10. trapezoid WXYZ with vertices W(�1, 3),E(4, 3), and F(2, 0) X(�1, �4), Y(�5, �4), and Z(�3, 3)

y

xO

y

xO

y

xO

y

xO

7MG3.2

Determine whether each figure has line symmetry. If so, copy thefigure and draw all lines of symmetry.

1. 2. 3.

4. 5. 6.

7. Graph �ABC with vertices A(2, 2), 8. Graph square ABCD with vertices B(5, 4),and C(5, 1) and its reflection over A( �1, 2), B(2, �1), C(5, 2), and D(2, 5)the x-axis. Then find the coordinates and its reflection over the y-axis. Thenof the reflected image. find the coordinates of the reflected image.

The coordinates of a point and its image after a reflection are given.Describe the reflection as over the x-axis or y-axis.

9. B(1, �2) → B(1, 2) 10. J(�3, 5) → J(�3, �5) 11. W(�7, �4) → W(7, �4)

y

xO

y

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NAME ________________________________________ DATE ______________ PERIOD _____

PracticeReflections


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeReflections


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10-10

1. FLAGS The figure shows a flag similarto the national flag of Denmark. Howmany lines of symmetry does the flaghave? Draw all lines of symmetry.

2. FLAGS The figure shows a flag similarto the national flag of Switzerland.How many lines of symmetry does theflag have? Draw all lines of symmetry.

3. INTERIOR DESIGN An interior designerhas been hired to decorate a room thathas the shape of a regular hexagon.Before beginning work, the designerstudies the symmetry of the room. Howmany lines of symmetry does the roomhave? Draw all lines of symmetry onthe figure.

4. ASTROLOGY The figure shows theastrological symbol for Sagittariusplotted on a coordinate system. Reflectthe symbol across the x-axis. Graph thereflected image.

y

xO

5. ARCHITECTURE A corporate plaza is tobe built around a small lake. Building 1has already been built. Suppose thereare axes through the lake as shown.Show where Building 2 should be builtif it will be a reflection of Building 1across the y-axis followed by areflection across the x-axis.

y

xO

Building 1

Lake

6. ARCHITECTURE Use the informationfrom Exercise 5. Suppose that a thirdbuilding is to be built as shown. Tocomplete the business park, showwhere a fourth building should be builtif it is a reflection of Building 3 acrossthe x- and y-axis.

y

xO

Building 1Building 3

Lake

7MG3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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The Twelve Dot PuzzleIn this puzzle, a broken line made up of 5 segments must pass through each of 12 dots. The line cannot go through a dot more than once, although it may intersect itself. The line must start at one dot and end at a different dot.

One solution to this puzzle is shown at the right. Two solutions to the puzzle are not “different” if one is just a reflection or rotation of the other.

Find 18 other solutions.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18.

7MG3.2

Exercises

Example

NAME ________________________________________ DATE ______________ PERIOD _____

TI-73 ActivityLines of Symmetry


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10-10

Draw polygons on the calculator by entering the coordinates of the vertices. Use the DRAWfeature to check for vertical and/or horizontal lines of symmetry.

The vertices of a polygon are: (1, 2), (7, 2), (7, 4), (4, 7), and (1, 4). Draw thepolygon and tell whether it has vertical and horizontal lines of symmetry.

Step 1 Clear all lists.

[MEM] 6

Step 2 Enter the x-coordinates in L1. Enter the y-coordinates in L2. Repeat the first value at theend of each column.

Step 3 Create Plot1.

[PLOT] 4

[PLOT] 1

Step 4 Choose L1 and L2, if not already chosen.

[STAT] [STAT]

Step 5 Set the graph window and display the plot.

4

Step 6 Draw a vertical line through the polygon. Use the arrow keys to center the line.

4

This polygon has a vertical line of symmetry.

Draw each polygon on the calculator and find any vertical or horizontal lines ofsymmetry.

1. (1, 5) 2. (10, 3)(4, 1) (6, 6)(4, 9) (2, 3)

3. (5, 3) 4. (2, 6)(1, 1) (4, 1)(8, 1) (7, 1)(12, 3) (9, 6)

DRAW

ZOOM

ENTER2ndENTER2nd

ENTERENTER2nd

ENTER2nd

LIST

ENTER2nd

Pre-AP

NAME ________________________________________ DATE ______________ PERIOD _____

Student Recording SheetUse this recording sheet with pages 568–569 of the Student Edition.


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Read each question. Then fill in thecorrect answer.

1.

2.

3.

4.

5.

6.

7.

8.

9.

Record your answers for Question 10 onthe back of this paper.

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

10

Ass

essm

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General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she

arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.

Exercise 10 Rubric

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


10 Rubric for Scoring Pre-AP(Use to score the Pre-AP question on page 569 of the Student Edition.)

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Score Specific Criteria4 �J is correctly identified as an obtuse angle, and �M is correctly identified as an

acute angle. The polygon is correctly identified as a parallelogram. An accurateexplanation that the polygon can be used by itself to make a tessellation is given.The coordinates of the translated figure are correctly determined to be J�(�1, 0),K�(�2, �4), L�(0, �4), and M�(1, 0). The coordinates of the reflection are correctlydetermined to be J�(�3, 5), K�(�4, �1), L�(�2, �1), and M�(�1, �5).

3 The identifications and the coordinates of the translation and the reflection arecorrect, but the explanation is not complete or not given. ORThe explanation and the coordinates of the translation and the relection are correct,but one of the identifications is not correct. ORThe identifications and the explanation are correct, but a mistake is made indetermining the coordinates of one or two vertices of the translated or reflectedfigure.

2 The identifications and the explanation are correct, but either the translation or the reflection is incorrect. ORThe explanation, translation, and reflection are corrrect, but two or three of theidentifications are incorrect.

1 The identifications are correct, but the explanation, translation, and reflection areincorrect. ORThe explanation is correct, but the identifications, translation, and reflection areincorrect. ORThe translation is correct, but the identifications, explanation, and reflection areincorrect. ORThe reflection is correct, but the identifications, explanation, and translation areincorrect.

0 Response is completely incorrect.

1. The circle graph showshow Enzo spends his day.Which activity does he spend most of his time doing? 1.

Classify each pair of angles as complementary, supplementary,or neither.

2. 3. 2.

3.

Label the angles as vertical or adjacent.4. 5. 4.

5.3 42

1

145˚35˚

53˚37˚

Daily Activities

20%Entertainment

30%Sleeping20%

Working

10%Eating

5%Dining 15%

Other

Find the missing measure in each triangle. Then classifythe triangle as acute, right, or obtuse.

1. 2. 1.

2.

ALGEBRA Find the missing angle measure in each quadrilateral.

3. 4. 3.

4.

5. MULTIPLE CHOICE The first three rows in a theater have 24 seats, 28 seats, and 34 seats, respectively.If the fifth row has 52 seats, how many seats does the fourth row have?A. 38 B. 40 C. 42 D. 0 5.

114˚

73˚

112˚

x˚50˚

x˚

23˚

29˚x˚

55˚

62˚

x˚


Chapter 10 Quiz 1(Lessons 10-1 through 10-3)

Chapter 10 Quiz 2(Lessons 10-4 through 10-6)

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NAME ________________________________________ DATE ______________ PERIOD _____

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1. A photo that is 3 inches wide by 6 inches long will be resized to fit in a space that is 2 inches wide. How long will the resized photo be? 1.


2. 3. 2.

3.Determine whether each figure is a polygon. If it is,classify the polygon and state whether it is regular. 4.If it is not a polygon, explain why.

4. 5. 5.

9 cm

2 cm

x3 cm

6 ft

3 ft1.5 ftx

1. Triangle ABC with vertices A(2, 4), B(3, �2), and C(�5, 1) 1.is translated 4 units left and 3 units up. What are the coordinates of B�?

2. Quadrilateral DEFG has vertices D(3, �1), E(7, �1), 2.F(8, �4), and G(1, �3). Find the vertices of D�E�F�G�after a translation of 2 units left and 6 units up.

3. Determine whether the figure at the right has line symmetry. Write yes or no. If yes, then draw all lines of symmetry. 3.

4. Triangle XYZ has vertices X(�10, 4), Y(�8, �2), and Z(�6, 0). 4.It is reflected over the x-axis. What are the coordinates of X�?

5. Parallelogram ABCD has vertices A(�3, 2), B(�1, 4),C(�1, �1), and D(�3, �3). Graph the figure and its reflection over the y-axis. Then find the coordinates of its reflected image.

5.


Chapter 10 Quiz 3(Lessons 10-7 and 10-8)

Chapter 10 Quiz 4(Lessons 10-9 and 10-10)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

10

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Write the letter for the correct answer in the blank at the right of each question.

1. MONEY The following circle graph shows where the United States government spends its money.On what do they spend the most money?A. Interest on Public Debt C. DefenseB. Social Security D. Health 1.

2. Angle 1 and angle 2 are supplementary.If m�1 � 27�, find m�2.F. 27� H. 73�

G. 63� J. 153� 2.

3. Determine which property is not a characteristic of a trapezoid.A. one pair of parallel sides C. need not have a right angleB. quadrilateral D. 4 congruent sides 3.

Classify each angle as acute, right, obtuse, or straight.

4. 5. 6. 4.

5.

6.Classify each pair of angles as supplementary,complementary, or neither.

7. 8. 7.

8.


9. 10. 9.

10.

Classify each quadrilateral using the name that best describes it.

11. 12. 11.

12.

48˚48˚110˚70˚

U.S. Money Expenditures

22%Interest

on PublicDebt

21%Health

16%Defense(Military)

16%Other

25%Social

Security

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10NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 10 Mid-Chapter Test(Lessons 10-1 through 10-6)

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NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


10 Chapter 10 Vocabulary Test

Choose the correct term to complete each sentence.

1. Degrees are the unit of measure for (angles, lengths). 1.

2. Two angles are (complementary, supplementary) angles if 2.the sum of their measures equals 90�.

3. A scalene triangle has (two, no) congruent sides. 3.

4. A rhombus is a parallelogram with (four, two) congruent sides. 4.

5. A pentagon is a polygon with (six, five) sides. 5.

6. A (tessellation, transformation) is a repetitive pattern of 6.polygons that fit together with no overlaps or holes.

7. A line of symmetry is used with a (translation, reflection). 7.

8. An (acute, obtuse) angle has a measure between 90� and 180�. 8.

9. Congruent angles have the same (sides, measure). 9.

10. A polygon is formed by (three, two) or more straight lines. 10.

Define each term in your own words.

11. parallel

12. indirect measurement

acute angle anglecircle graphcomplementary anglescongruent anglescongruent figuresdegreeshexagonindirect measurementline of symmetry

line symmetryobtuse angleoctagonparallelogrampentagonpolygonquadrilateralreflectionregular polygonrhombus

right anglesimilar figuresstraight anglesupplementary anglestessellationtransformationtranslationtrapezoidtrianglevertex


1. The measure of an angle is 45�. Classify the angle.A. acute B. straight C. obtuse D. right 1.

2. ALGEBRA If �P and �Q are complementary and the measure of �P is 40°,what is the measure of �Q?F. 40° G. 50° H. 60° J. 140° 2.

3. What is the angle measure for a section in a circle graph that represents 25%?A. 9° B. 25° C. 90° D. 335° 3.

4. OLYMPICS The table shows the results of a student survey. On a circle graph of the data, which section would have an angle measure of 180�?F. Bobsled H. SkiingG. Skating J. Curling 4.

For Questions 5 and 6, classify each pair of angles.

5. 6. 5.

A. complementary F. complementaryB. supplementary G. supplementaryC. right H. rightD. no relationship J. no relationship 6.

7. Which figure is a polygon? A. B. C. D. 7.

8. Which figure is a regular polygon?F. G. H. J. 8.

9. Which pair of figures is similar?A. B. C. D. 9.

10. Find the value of x in the pair of similar figures.F. 4 H. 2G. 3 J. 1 10.

1234˚ 146˚

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10NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 10 Test, Form 1C

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Favorite WinterOlympic Events

Number of Students

Bobsled 12Skating 30Skiing 45Curling 3

7

3 4

546

3 2

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1 cm

11. Classify the quadrilateral using the name that best describes it.A. square C. trapezoidB. parallelogram D. rhombus 11.

12. Classify the triangle by its angles and by its sides.F. acute, equilateral H. obtuse, isoscelesG. right, equilateral J. obtuse, equilateral 12.

13. Classify the quadrilateral using the name that best describes it.A. rhombus C. squareB. rectangle D. trapezoid 13.

14. Which regular polygon can be used by itself to make a tessellation?F. pentagon G. octagon H. square J. decagon 14.

15. Find the coordinates of J� after �HIJ is translated 2 units down.A. (2, 4) C. (0, 5)B. (0, 2) D. (2, 3) 15.

16. Parallelogram ABCD with vertices A(�5, 2), B(�4, 4),C(�1, 4), and D(�2, 2) is translated 3 units right and 4 units up. What are the coordinates of A�?F. (�8, �2) G. (�2, 6) H. (2, 6) J. (3, 4) 16.

17. Find the coordinates of �T�U�V� with vertices T(2, 2), U(5, 4), V(5, 2) after a reflection over the y-axis.A. T�(�2, 2), U�(�5, 4), V�(�5, 2) C. T�(2, 2), U�(4, 5), V�(2, 5)B. T�(2, �2), U�(5, �4), V�(5, �2) D. T�(2, �2), U�(5, �4), V�(�5, �2) 17.

18. Choose the figure that shows all lines of symmetry drawn correctly.F. G. H. J. 18.

19. ART An artist is using right triangles in her design. If all the triangles have an angle measure of 24°, what is the measure of the third angle? A. 66° B. 76° C. 106° D. 156° 19.

20. BOOKS Brooke, Mia, and Orlando are reading a mystery, fiction, and comic book, but not in that order. Mia does not care for fiction books.Orlando does not read fiction or comic books. Which is a true pairing? F. Brooke, fiction H. Mia, fictionG. Brooke, mystery J. Orlando, comic book 20.

Bonus Name the regular polygon if the sum of the measures of the polygon is 1,440� and the measure of one angle is 144�. B:

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10 Chapter 10 Test, Form 1 (continued)C

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1. The measure of an angle is 95�. Classify the angle.A. acute B. right C. straight D. obtuse 1.

2. ALGEBRA If �W and �X are complementary and the measure of �W is 56°,what is the measure of �X?F. 34° G. 44° H. 104° J. 124° 2.

3. What is the angle measure for a section in a circle graph that represents 38%?A. 38° B. 68° C. 137° D. 322° 3.

4. OLYMPICS The table shows the results of a student survey. On a circle graph of the data, which section would have an angle measure of 48�?F. Bobsled H. SkiiingG. Skating J. Curling 4.


5. 6. 5.


7. Which figure is a polygon? A. B. C. D. 7.

8. Which figure is a regular polygon? F. G. H. J. 8.

9. Choose the pair of similar figures.A. B. C. D. 9.

10. Find the value of x in the pair of similar figures.F. 1.5 H. 2.5G. 2 J. 3 10.5 m

2 m 2 m 1 m1.5 m1.5 m

1 m

3 m 3 m

x m

2

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1

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10NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 10 Test, Form 2AC

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BobsledSkatingSkiingCurling

Number ofStudents


3453012

136

4

11. Classify the quadrilateral using the name that best describes it.A. rhombus C. parallelogramB. square D. trapezoid 11.

12. Classify the triangle by its angles and by its sides.F. right, isosceles H. obtuse, isoscelesG. acute, isosceles J. acute, equilateral 12.

13. Classify the quadrilateral using the name that bestdescribes it.A. square C. parallelogramB. trapezoid D. rectangle 13.

14. Which regular polygon can be used by itself to make a tessellation?F. octagon H. equilateral triangleG. decagon J. circle 14.

15. Find the coordinates of H�after �HIJ is translated 5 units down.A. (�3, 5) C. (�8, �1)B. (�6, �3) D. (�3, �6) 15.

16. Parallelogram ABCD with vertices A(�3, �1), B(2, �1), C(1, �3), andD(�4, �3) is translated 4 units left and 8 units up. What are thecoordinates of C�?F. (�4, 8) G. (�3, 5) H. (�5, 5) J. (5, �3) 16.

17. Find the coordinates of �T�U�V� with vertices T(�1, 2), U(1, �1),V(�3, �2) after a reflection over the x-axis.A. T�(�1, �2), U�(1, 1), V�(�3, 2) C. T�(1, 2), U�(�1, �1), V�(3, �2)B. T�(1, �2), U�(�1, 1), V�(3, 2) D. T�(2, �1), U�(�1, 1), V�(�2, �3) 17.


19. ART An artist is using right triangles in her design. If all the triangles have an angle measure of 68�, what is the measure of the third angle? A. 22� B. 32� C. 112� D. 122� 19.

20. BOOKS Brenna, Leslie, John, and Wesley are reading a mystery (M),fiction (F), biography (B), and comic book (C), but not in that order. Brennadoes not like mystery, fiction, or comic books. Neither Leslie nor John likesmysteries. Leslie does not like comic books. Which is a true pairing? F. Brenna (F) G. Leslie (M) H. John (C) J. Wesley (B) 20.

Bonus Name the regular polygon if the sum of the measures of the polygon is 3,240� and the measure of one angle is 162�. B:

NAME ________________________________________ DATE ______________ PERIOD _____


10 Chapter 10 Test, Form 2A (continued)C

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1. The measure of an angle is 89�. Classify the angle.A. acute B. right C. straight D. obtuse 1.

2. ALGEBRA If �M and �N are supplementary and the measure of �M is 74�, what is the measure of �N?F. 16° G. 26° H. 106° J. 126° 2.

3. What is the angle measure for a section in a circle graph thatrepresents 47%?A. 47° B. 85° C. 169° D. 313° 3.

4. OLYMPICS The table shows the results of a student survey. On a circle graph of the data, which section would have an angle measure of 120�?F. Bobsled H. SkiingG. Skating J. Curling 4.


5. 6. 5.


7. Which figure is a polygon?A. B. C. D. 7.

8. Which figure is not a regular polygon? F. G. H. J. 8.

9. Choose the pair of similar figures.A. B. C. D. 9.

10. Find the value of x in the pair of similar figures.F. 1.5 H. 3.5G. 3 J. 14 10.

4

2

5

3

27 3

14 2510

12

21

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10NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 10 Test, Form 2BC

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Number ofStudents

Bobsled 12Skating 30Skiing 45Curling 3

117

9

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4

7 m

2 m

2 m6 m

6 m 1 m

1 m3 m3 m x m

11. Classify the quadrilateral using the name that best describes it.

A. quadrilateral B. rhombus C. trapezoid D. parallelogram 11.

12. Classify the triangle by its angles and by its sides.F. obtuse, scalene G. right, isosceles H. right, scalene J. acute, scalene 12.

13. Classify the quadrilateral using the name that best describes it.A. trapezoid C. parallelogramB. rhombus D. square 13.

14. Which regular polygon can be used by itself to make a tessellation?F. octagon G. hexagon H. heptagon J. circle 14.

15. Find the coordinates of I� after �HIJ is translated 5 units down.A. (�1, �2) C. (�2, �2)B. (�2, 2) D. (�2, �1) 15.

16. Parallelogram ABCD with vertices A(�3, �1), B(2, �1),C(1, �3), and D(�4, �3) is translated 4 units left and 8 units up. What are the coordinates of B�?F. (�2, 7) G. (�2, 8) H. (2, 9) J. (10, �5) 16.

17. Find the coordinates of �T�U�V� with vertices T(�1, 2), U(1, �1), V(�3, �2) after a reflection over the y-axis.A. T�(�1, �2), U�(�1, �1), V�(�3, 2) C. T�(�1, �2), U�(1, 1), (�3, 2)B. T�(2, �1), U�(�1, 1), (�2, �3) D. T�(1, 2), U�(�1, �1), (3, �2) 17.


19. ART An artist is using right triangles in her design. If all the triangles have an angle measure of 58�, what is the measure of the third angle? A. 22° B. 32� C. 112� D. 122� 19.

20. BOOKS Brenna, Leslie, John, and Wesley are reading a mystery, fiction,biography, and comic book, but not in that order. Wesley does not likemystery, fiction, or comic books. Neither Leslie nor John likes mysteries.Leslie does not like comic books. Which is a true pairing? F. Brenna, fiction H. John, fictionG. Leslie, biography J. Wesley, biography 20.

Bonus Name the regular polygon if the sum of the measures of the polygon is 2,520� and the measure of one angle is 157.5�. B:

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10 Chapter 10 Test, Form 2B (continued)C

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1. Draw an angle having a measurement of 180�. Then classify 1.the angle as acute, obtuse, right, or straight.

For Questions 2 and 3, name each angle in four ways. Then classify the angle as acute, right, obtuse, or straight. 2.

2. 3.

3.

4. MONEY For the following table, find the number of degrees for each section of a circle graph. Then make a circle graph of the data.

5. ALGEBRA If �R and �S are complementary and �S is 82°,what is the measure of �R? 4.

6. Find the value of x in the figure. 5.

6.


7. 8. 7.

8.

Classify each quadrilateral using the name that bestdescribes it.

9. 10. 9.

10.

11. Find the missing angle measure. 11.147˚

40˚ 90˚

x˚

37˚

53˚

x˚

28˚

35˚

x˚

98˚x˚

Bills in Circulation

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10NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 10 Test, Form 2CC

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Bobsled 12Bobsled12

Type of Bills Number of Bills inCirculation (trillions)

$1 bills 6$5 bills 1

$10 bills 1$20 bills 4

12. Determine whether the pair of figures is

similar. Justify your answer. 12.

13. Find the value of x in thepair of similar figures. 13.

For Quesions 14 and 15, find the 14.measure of an angle in each polygon.

14. regular pentagon 15. regular octagon 15.

16. Triangle ABC has vertices A(1, 2), B(�2, 3), and C(0, �3).Find the vertices of �A�B�C� after a translation of 4 units right and 2 units up. Then graph the figure and its translated image. 16.

17. Point W (1, 3) is reflected to its image W� (1, �3). Describe the reflection as over the x-axis or y-axis. 17.

18. Draw all lines of symmetry for an equilateral triangle. 18.

19. ALGEBRA Find m�G in �FGH if m�F � 47° and m�H � 65°. 19.

20. FOOD For lunch Avery, Nathan, Alex, and Takara ordered tacos, a salad, fish sandwich, and pasta, but not in that order.Nathan does not like fish, tacos, or salad. Neither Alex nor Takara likes fish. Takara does not like tacos. Find the food that each person ordered. 20.

Bonus Can a regular polygon with an angle measure of 160� be used by itself to make a tessellation? Explain. B:

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10 Chapter 10 Test, Form 2C (continued)C

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1. Draw an angle having a measurement of 90�. Then classify the angle as acute, obtuse, right, or straight. 1.

For Questions 2 and 3, name each angle in four ways. Then classify the angle asacute, right, obtuse, or straight.

2. 3. 2.

3.


5. ALGEBRA If �C and �D are supplementary and �D is 70°,

4.

what is the measure of �C? 5.



7. 8. 7.

8.


9. 10. 9.

10.

11. Find the missing angle measure. 11.

80˚

100˚

135˚x˚

42˚48˚

x˚88˚

29˚ x˚

46˚x˚

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10NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 10 Test, Form 2DC

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Type of Bills Number of Bills inCirculation (trillions)

$5 bills 1$10 bills 1$20 bills 4

$100 bills 3

12. Determine whether the pair of figures is similar. Justify your answer.

12.

13. Find the value of x in the 13.pair of similar figures.

For Questions 14 and 15, find the measure of an angle in each polygon. 14.

14. regular hexagon 15. regular nonagon 15.

16. Triangle ABC has vertices A(1, 2), B(�2, 3), and C(0, �3).Find the vertices of �A�B�C� after a translation of 2 units left and 3 units up. Then graph the figure and its translated 16.image.

17. Point X(3, 5) is reflected to its image X�(�3,5). Describe the reflection as over the x-axis or y-axis. 17.

18. Draw all lines of symmetry for a square. 18.

19. ALGEBRA Find m�S in�STU if m�T � 59° and m�U � 70°. 19.

20. FOOD For lunch Avery, Nathan, Alex, and Takara ordered tacos, salad, fish sandwich, and pasta, but not in that order.Avery does not like fish, tacos, or salad. Neither Alex nor Takara likes fish. Takara does not like tacos. Find the food that each person ordered. 20.

Bonus Can a regular polygon with an angle measure of 135� be used by itself to make a tessellation? Explain. B:

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NAME ________________________________________ DATE ______________ PERIOD _____


10 Chapter 10 Test, Form 2D (continued)C

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1. Draw an angle having a measurement of 147�. Then classifythe angle as acute, obtuse, right, or straight. 1.

For Questions 2 and 3, name each angle in four ways.Then classify the angle as acute, right, obtuse, or straight.

2. 3. 2.

3.


5. ALGEGBRA If �A and �B are supplementary and m�A�108.5°, 5.what is m�B?



7. 8. 7.

8.


9. 10. 9.

10.

11. Find the missing angle measure. 11.110˚ x˚

37˚ 32˚

x˚

37˚x˚

76˚

x˚


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10NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 10 Test, Form 3C

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Type of Bills Number of Bills inCirculation (billions)

$1 bills 6,400

$2 bills 600

$5 bills 1,500

$10 bills 1,300

$20 bills 4,100

$50 bills 900

$100 bills 2,900 4.

12. Determine whether the pair 12.of figures is similar. Justify your answer.

13. Find the value of x in the pair 13.of similar figures.

For Questions 14 and 15, find the measure of an angle in each polygon. 14.

14. regular decagon 15. regular 18-gon 15.

16. Triangle ABC has vertices A(1, 2), B(�2, 3), and C(0, �4).The vertices of �A�B�C� after a translation are A�(�3, 5),B�(�6, 0), and C�(�4, �1). Describe the translation. 16.

17. Parallelogram WXYZ has vertices W(�1, 2), X(3, 2),Y(1, �1), and Z(�3, �1). Graph the figure and its reflected image over the y-axis. Then find the coordinates of the reflected image. 17.

18. Draw all lines of symmetry for a regular pentagon. 18.

19. ALGEBRA Find m�S in �STU if m�T � 19.8°and m�U � 65.4°. 19.

20. SPORTS Avery, Nathan, Alex, and Takara are on the following teams: basketball, swimming, soccer, and gymnastics, but not necessarily in that order. Neither Alex nor Nathan do gymnastics. Takara holds a record in swimming. Alex may play soccer next year. Who is on which team? 20.

Bonus Can a regular polygon with an angle measure of 120° be used by itself to make a tessellation? Explain. B:

y

xO

1 ft4 ft

3 ft

0.5 ft 2 ft0.75 ft

1.5 ftx

6 mm3 mm

5 mm2 mm

NAME ________________________________________ DATE ______________ PERIOD _____


10 Chapter 10 Test, Form 3 (continued)C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solutions in more than one way orinvestigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.

1. a. Draw a figure that is a polygon and another figure that is not apolygon. Explain how the figures are different.

b. Explain how to classify triangles by the measure of their angles. Drawan example of each classification.

c. Describe at least four classifications of quadrilaterals. Draw anexample of each.

d. Is a trapezoid ever a rhombus? Explain your reasoning.

e. Explain what is meant by regular polygon.

f. Draw a right angle, obtuse angle, straight angle, and acute angle.Explain how the figures are different.

g. Draw an example of supplementary angles. Explain howsupplementary angles are different from complementary angles.

2. a. Explain why you think honeycombs are tessellated with hexagonsinstead of octagons.

b. Tile a rectangular area with squares. Then use at least twotranslations to create an Escher-like drawing. Explain each step.

3. a. Draw a figure that has two or more lines of symmetry. Draw all thelines of symmetry.

b. Draw a figure that has no lines of symmetry.

135˚135˚

90˚

120˚

120˚120˚

Ass

essm

ent


10NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 10 Extended-Response Test

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

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1. GEOMETRY What is the area of the rectangle? (Lesson 3-6)

A 5 m2 C 7.14 m2

B 6.5 m2 D 13 m2 1.

2. Write �383�

as a decimal using bar notation. (Lesson 4-5)

F 24.2�4� G 0.24� H 0.2�4� J 0.2�4�2� 2.

3. Find 3�13� � 3�

29�. Write in simplest form. (Lesson 5-3)

A 6�14� B 6�

13� C 6�

59� D 7�

29� 3.

4. Write �23� as a percent to the nearest hundredth. (Lesson 6-8)

F 0.67% G 1.67% H 66.33% J 66.67% 4.

5. Estimate 26% of 319. (Lesson 7-3)

A 100 B 80 C 32 D 8 5.

6. COLLECTIONS Jamilla bought six new frog figurines to add to her collection. This is 24% of the previous number she originally owned. How many figurines did she originally have in her collection? (Lesson 7-5)

F 25 G 24 H 18 J 15 6.

7. What is the range of the data in the line plot?(Lessons 8-1)

A 45 C 15B 44.8 D 9 7.

8. ATTENDANCE The following set of data lists the number of students in the seventh-grade classes at Smith Valley Middle School: 25, 22, 23, 18, 21, 17. Find the median of the number of students in the seventh-grade classes. (Lesson 8-2)

F 20 G 20.5 H 21 J 21.5 8.

9. WEATHER The probability that it rains today is �1285�. Find

the probability that it will not rain today. (Lesson 9-2)

A 7% B 18% C 28% D 72% 9.

10. CLOTHES Bob bought 2 button-down shirts, 3 ties, 2 pairs of socks, and 3 pairs of pants. How many different outfits can Bob make with his new clothes, choosing one of each? (Lesson 9-3)

F 36 G 15 H 10 J 4 10. F G H J

A B C D

F G H J

A B C D

��

�

�

� � � ��

40 4241 4443 4645 47 48 49

�

50 51

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F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


10 Standardized Test Practice(Chapters1–10)

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

1.4 m

5.1 m

11. DECORATING How many different ways can 7 different candles be arranged in a line on a shelf? (Lesson 9-4)

A 42 C 5,040 B 840 D 40,320 11.

12. Out of 20 rolls of a number cube, Mark rolls a 4 five times.What is the experimental probability of rolling a 4? (Lesson 9-7)

F �210� H �

14�

G �15� J �

45� 12.

13. The measure of an angle is 135�. Classify the angle.(Lesson 10-1)

A acute C obtuseB straight D right 13.

14. SCHOOL Sam has his own small chalkboard similar in shape to the one at school. Find the missing measurement of Sam’s chalkboard. (Lesson 10-7)

F 1.1 H 2.2G 2 J 3.3 14.

15. Use the graph to tell what type of transformation is shown.(Lessons 10-9 and 10-10)

A translationB reflection over the x-axisC reflection over the y-axisD no movement 15.

16. How many ways can Antoine choose 3 music boxes from a collection of 20? (Lesson 9-5)

F 6 H 123G 60 J 1,140 16.

17. Find the third angle of a right triangle if the measure of one of the angles is 55°. (Lesson 10-4)

A 125 C 45B 80 D 35 17. A B C D

F G H J

A B C D

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10NAME ________________________________________ DATE ______________ PERIOD _____

Standardized Test Practice (continued)

(Chapters 1–10)

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

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18. Find �35 (�5). (Lesson 2-8) 18.

19. Write the ratio 15.5 per 100 as a percent. (Lesson 4-6) 19.

20. Solve the proportion �35

� � �1x8�. (Lesson 6-4) 20.

21. FURNITURE Find the total price to the nearest cent of an office chair that costs $165 with a sales tax of 7%. (Lesson 7-8) 21.

22. Make a line plot of laundry detergent prices: 22.$5.50, $8.50, $7, $6, $5.50, $8, $6. (Lesson 8-1)

23. Omari’s assignment for art class is to complete 4 projectsfrom a list of 6. In how many ways can Omari do this if theorder in which he does them is not important? (Lesson 9-5) 23.

24. Classify the quadrilateral using the namethat best describes it. (Lesson 10-6) 24.

25. Triangle XYZ has vertices X(2, �1), Y(4, �3), and Z(1, �4). The translated figure �X�Y�Z� has vertices X�(�1, 4), Y�(1, 2), and Z�(�2, 1). (Lesson 10-9)

a. Graph the figure and its translated image. 25a.

b. Describe the translation. 25b.

c. Write the translation as an ordered pair. 25c.

y

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Part 2: Short Response

Instructions: Write answers to short response in the space provided.

NAME ________________________________________ DATE ______________ PERIOD _____


11 Standardized Test Practice (continued)

(Chapters 1–10)

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

An

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10

Chapter Resources

Answers (Anticipation Guide and Lesson 10-1)

Chapter 10 A1 Glencoe California Mathematics, Grade 6

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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

10-1

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Answers (Lesson 10-1)


An

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10-1

1.C

LOC

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Th

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UA

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hen

a b

alle

t da

nce

r’s

feet

are

in f

irst

pos

itio

n,t

he

hee

ls a

re t

ouch

ing,

and

the

feet

are

tu

rned

ou

t.A

dan

cer

wit

h e

xcel

len

t te

chn

iqu

e ca

n p

osit

ion

his

or

her

fee

t so

th

at t

hey

are

nea

rly

in a

str

aigh

t li

ne.

Isab

ella

is

prac

tici

ng

her

tec

hn

iqu

e.C

lass

ify

the

angl

e h

erfe

et f

orm

as

acu

te,o

btu

se,o

r ri

ght.

ob

tuse

6.PA

RK

ING

LO

TE

ric,

Rya

n,A

ish

a,an

d A

bbey

are

all

par

ked

in t

he

sch

ool

lot.

Wh

o is

par

ked

at a

djac

ent

angl

es f

rom

one

anot

her

?

Eri

c an

d R

yan

;R

yan

an

d

Ab

bey

;A

bb

ey a

nd

Ais

ha;

Ais

ha

and

Eri

c

Aish

a

Ryan

Eric

Abbe

y

6MG

2.1

Nam

e ea

ch a

ngl

e in

fou

r w

ays.

Th

en c

lass

ify

the

angl

e as

acu

te,r

igh

t,ob

tuse

,or

stra

igh

t.

1.2.

3.

�4,

�S

,�R

ST

,�

2,�

Y,�

XY

Z,

�1,

�B

,�C

BA

,�

TS

R;

ob

tuse

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YX

;ri

gh

t�

AB

C;

stra

igh

t

4.5.

6.

�3,

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,�H

FG

,�

7,�

P,�

JPM

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6,�

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ED

F,�

GF

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acu

te

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PJ;

acu

te�

FD

E;

rig

ht

Use

th

e fi

gure

at

the

righ

t to

an

swer

Qu

esti

ons

7 an

d 8

.

7.N

ame

two

angl

es t

hat

are

ver

tica

l.�

MP

L,�

NP

O o

r �

MP

N,�

LP

O

8.N

ame

two

angl

es t

hat

are

adj

acen

t.�

LP

M,�

MP

N o

r �

MP

N,�

NP

O�

NP

O,�

OP

L o

r �

OP

L,�

LP

M

Use

th

e fi

gure

at

the

righ

t to

nam

e th

e fo

llow

ing.

9.tw

o ac

ute

an

gles

�D

CH

,�JB

D10

.tw

o st

raig

ht

angl

es�

AB

D,�

EB

G11

.tw

o ri

ght

angl

es�

AB

E,�

GB

C12

.tw

o ob

tuse

an

gles

�F

GE

,�A

CH

FG

CB E

AD

H

J

P

LM

ON

6E

D

F7M

P

J3

H

GF

1C

BA

2X

Z

Y

4R

S

T

NA

ME

____

____

____

____

____

____

____

____

____

____

DA

TE

___

____

____

___

PE

RIO

D

____

_

Prac

tice

An

gle

Rel

atio

nsh

ips

Cha

pter

10

12G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-1

6MG

2.1

9–12

.Sam

ple

an

swer

s g

iven

.



NA

ME

____

____

____

____

____

____

____

____

____

____

DA

TE

___

____

____

___

PE

RIO

D

____

_

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pter

10

15G

lenc

oe C

alifo

rnia

Mat

hem

atic

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rade

6

Lesson 10–2

pygp

10-2

Get

Rea

dy

for

the

Less

on

Com

ple

te t

he

Min

i L

ab a

t th

e to

p o

f p

age

514

in y

our

text

boo

k.

Wri

te y

our

answ

ers

bel

ow.

1.C

lass

ify

the

angl

e as

acu

te,r

igh

t,ob

tuse

,or

stra

igh

t.ri

gh

t

2.C

opy

the

angl

e on

to a

pie

ce o

f pa

per.

Th

en d

raw

a r

ay

that

cu

ts t

he

angl

e in

to t

wo

con

gru

ent

angl

es.L

abel

th

ese

two

con

gru

ent

angl

es �

1 an

d �

2.

3.W

hat

is

m�

1 an

d m

�2?

45°

4.W

hat

is

the

sum

of

m�

1 an

d m

�2?

90°

5.C

opy

the

orig

inal

an

gle

onto

a p

iece

of

pape

r.T

hen

dra

w

a

ray

that

sep

arat

es t

he

angl

e in

to t

wo

non

-con

gru

ent

angl

es.L

abel

th

ese

two

angl

es �

3 an

d �

4.

6.W

hat

is

tru

e ab

out

the

sum

of

m�

3 an

d m

�4?

T

hey

eq

ual

90°

.

7.C

ompl

ete

Exe

rcis

es 1

–6 f

or t

he

angl

e sh

own

at

the

righ

t.st

raig

ht;

See

dia

gra

m;T

hey

are

eac

h 9

0°.;

180°

;S

ee d

iag

ram

;Th

e su

m is

180

°.

Rea

d t

he

Less

on

Fil

l in

th

e b

lan

ks

to a

nsw

er Q

ues

tion

s 8

and

9.

8.T

wo

angl

es a

re c

ompl

emen

tary

if

the

sum

of

thei

r m

easu

re i

s .

9.T

wo

angl

es a

re s

upp

lem

enta

ry i

f th

e su

m o

f th

eir

mea

sure

is

.

Rem

emb

er W

hat

Yo

u L

earn

ed10

.55

°11

.13

5°

45°

x°35

° x°

180°

90°

43

21

34

12

6MG

2.1,

6M

G2.

2Le

sson

Rea

ding

Gui

deC

om

ple

men

tary

an

d S

up

ple

men

tary

An

gle

s

An

gle

s in

Bas

ebal

lA

ngl

es p

lay

an i

mp

orta

nt

par

t in

man

y sp

orts

.In

bas

ebal

l,in

fiel

der

sst

and

on

an

d c

over

dif

fere

nt

par

ts o

f th

e in

fiel

d d

epen

din

g on

th

ep

osit

ion

of

the

run

ner

s.S

omet

imes

,a p

laye

r w

ill

hav

e to

tu

rn v

aryi

ng

angl

es t

o m

ake

pla

ys.

For

Exe

rcis

es 1

an

d 2

,loo

k a

t th

ese

pic

ture

s of

bas

ebal

l fi

eld

s.In

eac

hon

e,th

e fo

ur

infi

eld

ers

cove

r d

iffe

ren

t ar

eas

of t

he

dia

mon

d.U

se a

pro

trac

tor

to d

eter

min

e th

e m

easu

re o

f th

e an

gle

of t

he

area

cov

ered

by

the

2nd

bas

eman

wit

h d

iffe

ren

t ru

nn

er p

osit

ion

s.

1.2.

43°

26°

3.T

he

outf

ield

is

cove

red

by t

hre

e ot

her

pla

yers

:th

e le

ft,c

ente

r,an

d ri

ght

outf

ield

ers.

Th

e ar

eas

they

cov

er m

ay o

verl

ap s

ligh

tly

depe

ndi

ng

onw

hoe

ver

is c

lose

st t

o th

e ba

ll;b

ut

in g

ener

al,

each

pla

yer

has

an

are

a to

cov

er.T

his

fig

ure

sh

ows

the

area

mos

t of

ten

cov

ered

by

each

ou

tfie

lder

.Wh

at t

ype

of a

ngl

e do

es e

ach

are

a m

ake

wit

h h

ome

plat

e? W

hat

typ

e of

an

gle

do

all

thre

e ou

tfie

ld a

reas

com

bin

ed c

reat

e w

ith

h

ome

plat

e?ac

ute

;ri

gh

t4.

Du

rin

g a

gam

e,th

e pi

tch

er n

otic

es t

he

run

ner

on

sec

ond

base

wan

ts t

o st

eal

thir

d ba

se.I

f th

e pi

tch

er i

s fa

cin

g h

ome

plat

e,w

hat

typ

e of

an

gle

does

th

e pi

tch

er h

ave

to t

urn

th

rou

gh t

o th

row

th

e ba

ll t

o th

ird

base

?ri

gh

t5.

Du

rin

g a

diff

eren

t in

nin

g,a

run

ner

is

on f

irst

bas

e an

d ap

pear

s to

wan

tto

ste

al s

econ

d ba

se.W

hat

typ

e of

an

gle

does

th

e pi

tch

er n

eed

to t

urn

thro

ugh

to

thro

w t

he

ball

to

seco

nd

base

if

the

pitc

her

is

faci

ng

hom

epl

ate?

stra

igh

t

Hom

ePl

ate

Third

Base

Seco

ndBa

seAr

ea c

over

edby

righ

t fie

lder

Area

cov

ered

by c

ente

r fie

lder

Area

cov

ered

by le

ft fie

lder

Firs

tBa

se

Hom

ePl

ate

Third

Base

Seco

ndBa

seAr

ea c

over

ed b

y th

ese

cond

bas

eman

Firs

tBa

se

Hom

ePl

ate

Third

Base

Seco

ndBa

seAr

ea c

over

ed b

y th

ese

cond

bas

eman

Firs

tBa

se

NA

ME

____

____

____

____

____

____

____

____

____

____

DA

TE

___

____

____

___

PE

RIO

D

____

_

Enri

chm

ent

Cha

pter

10

14G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-1

6MG

2.1

Answers (Lessons 10-1 and 10-2)


An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DA

TE

___

____

____

___

PE

RIO

D

____

_

Cha

pter

10

17G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–2

10-2

Fin

d t

he

mis

sin

g an

gle

mea

sure

.

1.53

°2.

48°

3.65

°

4.48

°5.

95°

6.17

0°

7.70

°8.

94°

9.66

°

Use

th

e fi

gure

at

the

righ

t to

an

swer

Qu

esti

ons

10–1

3.

10.

Fin

d m

�H

JL

.15

0°

11.

�H

JL

and

�L

JM

are

wh

at t

ype

of a

ngl

es?

sup

ple

men

tary

12.

Fin

d m

�K

JM

.90

°

13.

�K

JL

and

�L

JM

are

wh

at t

ype

of a

ngl

es?

com

ple

men

tary

K JH

M

L

90°

30°

60°

24°

x°

43° 43

° x°

45°

65°

x°

10°

x°

85°

x°42

°

x°

25˚ x ˚

42˚

x ˚12

7˚

x˚

6MG

2.1,

6M

G2.

2Sk

ills

Prac

tice

Co

mp

lem

enta

ry a

nd

Su

pp

lem

enta

ry A

ng

les

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

10

16G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-2

Fin

d t

he

valu

e of

x.

Th

e tw

o an

gles

for

m a

rig

ht

angl

e or

90°

,so

they

are

com

plem

enta

ry,

Writ

e th

e eq

uatio

n.S

ubtr

act

43 f

rom

eac

h si

de.

so t

he

valu

e of

xis

47°

.

Fin

d t

he

valu

e of

x.

Th

e tw

o an

gles

for

m a

str

aigh

t li

ne

or 1

80°,

so t

hey

are

su

pple

men

tary

,

Writ

e th

e eq

uatio

n.S

ubtr

act

110

from

eac

h si

de.

so t

he

valu

e of

xis

70°

.

Fin

d t

he

valu

e of

xin

eac

h f

igu

re.

1.32

°2.

124°

3.95

°

4.19

°5.

45°

6.98

°

82°

x°45

°x°

71°

x°

85°

x°56

° x°

58°

x°

110

�x

�18

0�

110

�11

0x

�70

110˚

x

˚

43 �

x�

90�

43�

43x

�47

43° x°

•Tw

o an

gles

are

co

mp

lem

enta

ryif

the

sum

of

thei

r m

easu

re is

90°

.

m�

1 �

m�

2 �

90°

•Tw

o an

gles

are

su

pp

lem

enta

ryif

the

sum

of

thei

r m

easu

re is

180

°.

m�

3 �

m�

4 �

180°

•To

fin

d a

mis

sin

g a

ng

le m

easu

re,f

irst

dete

rmin

e if

the

angl

es a

re c

ompl

emen

tary

or

supp

lem

enta

ry.T

hen

writ

e an

equ

atio

n an

d su

btra

ct t

o fin

d th

e m

issi

ng m

easu

re.

34

12

Exam

ple

1

Exam

ple

2

Exer

cise

s

6MG

2.1,

6M

G2.

2St

udy

Guid

e an

d In

terv

entio

nC

om

ple

men

tary

an

d S

up

ple

men

tary

An

gle

s



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

10

19G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–2

pygp

10-2

1.SI

GN

Th

e su

ppor

t w

ire

for

a si

gn

mee

ts t

he

wal

l an

d th

e ov

erh

ang

assh

own

bel

ow.I

f m

�2

�42

°,fi

nd

m�

1.E

xpla

in y

our

reas

onin

g

m�

1 �

48°;

�1

and

�2

are

com

ple

men

tary

an

gle

s.

21

2.ST

REE

TSM

ain

Str

eet

inte

rsec

ts

Oak

Roa

d.If

a r

igh

t-h

and

turn

on

toO

ak R

oad

requ

ires

a 7

7°tu

rn,w

hat

degr

ee m

ust

a l

eft-

han

d tu

rn o

nto

O

ak R

oad

mak

e?

A le

ft h

and

tu

rn r

equ

ires

a

103°

turn

.

77˚Oa

k Ro

ad

Mai

n St

reet

3.R

AIL

RO

AD

Eas

t of

th

e to

wn

of

Roc

kpor

t,th

e ra

ilroa

d tr

acks

inte

rsec

t H

ighw

ay 6

7as

sh

own

bel

ow.I

f m

�1

�13

3°,f

ind

m�

2.E

xpla

in y

our

reas

onin

g.

m�

2 �

47°;

�1

and

�2

are

sup

ple

men

tary

an

gle

s.

1 2

4.C

AM

PIN

GJo

nn

a an

d E

liza

beth

fou

nd

ale

vel

cam

psit

e an

d pi

tch

ed t

hei

r te

nt

assh

own

bel

ow.I

f m

�1

�12

0°,f

ind

m�

2.E

xpla

in y

our

reas

onin

g.

m�

2 �

60°;

�1

and

�2

are

sup

ple

men

tary

an

gle

s.

21

5.G

AS

GA

UG

EB

elow

is

a pi

ctu

re o

f th

e ga

s ga

uge

in

Ser

gio'

s ca

r.T

he

angl

es m

ade

by t

he

indi

cato

r ar

eco

mpl

emen

tary

.If

the

m�

1 �

42°,

wh

at i

s th

e m

�2?

48°

FU

EL

EF

12

6.A

RC

HIT

ECTU

RE

Th

e pl

ans

for

a n

ewaq

uar

ium

cal

l fo

r se

vera

l h

allw

ays

ofex

hib

its

lead

ing

out

of a

cir

cula

r m

ain

room

.Bec

ause

of

the

size

of

the

tan

ksth

at w

ill

be u

sed,

the

angl

e fo

rmed

betw

een

tw

o ad

jace

nt

hal

lway

s ca

n b

en

o sm

alle

r th

an 6

5°.W

hat

is

the

max

imu

m n

um

ber

of h

allw

ays

that

can

be b

uil

t le

adin

g ou

t of

th

e m

ain

roo

m?

5

Mai

n

R

oom

Hallw

ay

Hallw

ay

65˚

6MG

2.1,

6M

G2.

2W

ord

Prob

lem

Pra

ctic

eC

om

ple

men

tary

an

d S

up

ple

men

tary

An

gle

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

10

18G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-2

Fin

d t

he

valu

e of

xin

eac

h f

igu

re.

1.68

°2.

115°

3.47

°

4.15

1°5.

70°

6.10

8°

Cla

ssif

y ea

ch p

air

of a

ngl

es a

s co

mp

lem

enta

ry,s

up

ple

men

tary

,or

nei

ther

.

7.8.

9.

com

ple

men

tary

nei

ther

sup

ple

men

tary

ALG

EBR

AF

ind

th

e va

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of x

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ach

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ure

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10.

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12.

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the

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the

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NA

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____

____

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____

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E _

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for

the

Less

on

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d t

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intr

odu

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t th

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p o

f p

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in y

our

text

boo

k.

Wri

te y

our

answ

ers

bel

ow.

1.E

xpla

in h

ow y

ou k

now

th

at e

ach

per

son

su

rvey

ed c

hos

e on

ly o

ne

shad

e of

blu

e.S

amp

le a

nsw

er:T

he

per

cen

ts a

dd

up

to

100

.

2.If

500

peo

ple

took

par

t in

th

e su

rvey

,how

man

y pr

efer

red

aqu

amar

ine?

85

Rea

d t

he

Less

on

3.In

th

e fo

llow

ing

circ

le g

raph

,wh

at i

s th

e pe

rcen

t re

pres

ente

d by

sect

ion

C?

How

do

you

kn

ow?

62.5

%;T

he

per

cen

ts m

ust

ad

d u

p t

o 1

00.

4.A

s st

ated

in

Exa

mpl

e 2

on p

age

519,

wh

en y

ou c

onst

ruct

a c

ircl

e gr

aph

,yo

u c

an c

hec

k yo

ur

wor

k by

mea

suri

ng

the

last

sec

tion

of

a ci

rcle

gra

ph

to v

erif

y th

at t

he

angl

es h

ave

the

corr

ect

mea

sure

s.W

hy

wil

l th

is w

ork

as a

ch

eck?

Sam

ple

an

swer

:If

th

e g

rap

h is

acc

ura

te t

hen

th

ela

st s

ecti

on

will

hav

e a

mea

sure

men

t co

rres

po

nd

ing

to

th

ep

erce

nt

rem

ain

ing

to

be

gra

ph

ed o

n t

he

circ

le.

Rem

emb

er W

hat

Yo

u L

earn

ed5.

If y

ou a

re g

iven

th

e re

sult

s of

a s

urv

ey a

nd

the

resu

lts

are

give

n i

npe

rcen

ts,h

ow d

o yo

u d

raw

a c

ircl

e gr

aph

to

repr

esen

t th

e re

sult

s of

th

esu

rvey

? D

escr

ibe

each

ste

p.S

amp

le a

nsw

er:

a.F

ind

th

e d

egre

es f

or

each

par

t.b

.Use

a c

om

pas

s to

dra

w a

cir

cle.

Th

en d

raw

a r

adiu

s.c.

Use

a p

rotr

acto

r to

dra

w t

he

ang

le t

hat

co

rres

po

nd

s to

eac

h p

erce

nt.

d.L

abel

eac

h s

ecti

on

of

the

gra

ph

.

Suc

cess

ful S

pac

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unch

es, 2

001

12.5

%B C

25% A

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AP

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Less

on R

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tist

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Dis

pla

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ata

in a

Cir

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Gra

ph

NA

ME

____

____

____

____

____

____

____

____

____

____

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____

____

____

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Mat

chst

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Puzz

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Th

e p

uzz

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on t

his

pag

e in

volv

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box

of

woo

den

mat

ches

.T

ooth

pic

ks

or a

ny

oth

er s

trai

ght

obje

cts

may

be

also

be

use

d.

Use

th

e sq

uar

e fi

gure

at

the

righ

t to

mak

e ea

ch o

f th

e fo

llow

ing

figu

res.

1.M

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2.M

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.3

iden

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mat

ches

to

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o m

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mak

e 2

squ

ares

.7

squ

ares

.(Yo

u m

ay c

ross

th

e m

atch

es i

n t

his

on

e on

ly.)

Use

th

e h

exag

onal

fig

ure

at

the

righ

t to

mak

e ea

ch o

f th

e fo

llow

ing

firg

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s.

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ove

4 m

atch

es t

o m

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6.M

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4 m

atch

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o m

ake

3 eq

uil

ater

al t

rian

gles

.4

iden

tica

l di

amon

ds.

Use

th

e sq

uar

e fi

gure

at

the

righ

t to

mak

e ea

ch o

f th

e fo

llow

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firg

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mat

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to

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mat

ches

to

mak

em

ake

5 id

enti

cal

squ

ares

.5

iden

tica

l sq

uar

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6MG

2.3



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ME

____

____

____

____

____

____

____

____

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____

____

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____

____

____

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____

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us.

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se a

pro

trac

tor

to d

raw

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86

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gle.

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is r

epre

sen

ts t

he

perc

ent

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nu

clea

r re

acto

rs i

n t

he

Un

ited

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tes.

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th

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ew r

adiu

s,dr

aw a

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angl

e fo

rF

ran

ce.R

epea

t th

is s

tep

for

the

oth

er t

wo

sect

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s.L

abel

eac

h s

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on a

nd

give

th

e gr

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a t

itle

.

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ING

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e ta

ble

show

s th

e n

um

ber

of m

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f th

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im t

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wh

o co

mpe

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swim

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ach

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pete

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on

ly o

ne

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ake

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ph o

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ta.

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clea

r R

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per

atio

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ted

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tes

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ries

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n13%

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nce

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that

sho

ws

data

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part

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hole

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le is

cal

led

a ci

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ph

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a c

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gra

ph,

the

perc

ents

add

up

to 1

00.

Whe

n pe

rcen

ts a

re n

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iven

, yo

u m

ust

first

det

erm

ine

wha

t pa

rt o

f th

e w

hole

each

item

rep

rese

nts.

Sw

im T

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tter

fly

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nt

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56%

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ple

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er C

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s

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ited

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tes

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nce

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s

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clea

r R

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per

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001

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Stud

y Gu

ide

and

Inte

rven

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Sta

tist

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pla

y D

ata

in a

Cir

cle

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ph



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

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ER

IOD

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___

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pter

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Lesson 10–3

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use

th

e ta

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th

at s

how

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en

um

ber

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peo

ple

th

at s

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k t

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five

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ited

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t of

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ph t

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sh

ows

the

data

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hin

ese,

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dar

in:

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di:

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glis

h:

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anis

h:

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gal

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°

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ph o

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bran

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mos

t h

alf

of t

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ited

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,200

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d Pr

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ract

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tist

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pla

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ata

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Cir

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ph

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

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ER

IOD

__

___

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pter

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hem

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EXPO

RTS

For

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rcis

es 3

an

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,use

th

e ci

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grap

h t

hat

sh

ows

the

per

cen

t of

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sian

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lfp

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leu

m e

xpor

ts b

y co

un

try

for

the

year

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.

3.W

hic

h c

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try

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th

e m

ost

petr

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m

expo

rts?

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aud

i Ara

bia

4.H

ow m

any

tim

es m

ore

expo

rts

does

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n

hav

e th

an Q

atar

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tim

es

DA

TA S

ENSE

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h g

rap

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e m

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ng

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es.

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lect

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aper

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sian

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f E

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rts

2003

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di

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bia

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hat

kin

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raig

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Mak

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Less

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th

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side

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rian

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are

con

gru

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ple

an

swer

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sam

e n

um

ber

of

tick

mar

ks o

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ach

of

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con

gru

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sid

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rite

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atio

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0 d

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5.If

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40˚

114˚

37˚

50˚

x˚

126˚

22˚

x˚51

˚

57˚

x˚

71˚

45˚

x˚

65˚

x˚38

˚

38˚x˚

49˚

x˚24

˚

36˚

x˚

81˚

84˚

x˚

6MG

2.2,

6M

G2.

3



An

swer

s

Tria

ng

le S

um

sT

he

mea

sure

s of

th

e an

gles

of

a tr

ian

gle

alw

ays

add

up

to 1

80°.

Th

esi

des

of a

tri

angl

e al

so h

ave

a sp

ecia

l re

lati

onsh

ip.I

n t

his

act

ivit

y,yo

u w

ill

expl

ore

the

rela

tion

ship

s of

th

e si

de l

engt

hs.

Cu

t th

e st

rips

of

pape

r fr

om t

he

righ

t si

de o

f th

is p

age.

Use

th

e 3

spec

ifie

d st

rips

for

eac

h p

robl

em.T

ell

if a

tri

angl

e ca

n b

e fo

rmed

wit

h t

hem

.If

so,t

ell

wh

at t

ype

of t

rian

gle

it i

s.1.

6 cm

,14

cm,a

nd

14 c

m

2.6

cm,6

cm

,14

cm

iso

scel

es t

rian

gle

no

t a

tria

ng

le

3.6

cm,8

cm

,14

cm4.

3 cm

,3 c

m,6

cm

no

t a

tria

ng

len

ot

a tr

ian

gle

5.3

cm,6

cm

,8 c

m6.

6 cm

,6 c

m,8

cm

scal

ene

tria

ng

leis

osc

eles

tri

ang

le

7.L

ook

at y

our

answ

ers

abov

e.C

hoo

se a

ny

set

of s

ide

len

gth

s th

at f

orm

atr

ian

gle.

Add

th

e tw

o sh

orte

st m

easu

res.

Com

pare

th

at s

um

wit

h t

he

lon

gest

sid

e le

ngt

h.T

ry t

his

wit

h a

ll t

he

tria

ngl

es a

bove

.Wh

at c

oncl

usi

onca

n y

ou m

ake

abou

t tr

ian

gle

side

len

gth

s?T

he

sum

of

the

len

gth

so

f an

y tw

o s

ides

of

a tr

ian

gle

is g

reat

er t

han

th

e le

ng

th o

fth

e th

ird

sid

e.

8.N

ow l

ook

at t

he

sets

of

side

len

gth

s th

at d

id n

ot f

orm

tri

angl

es.A

dd t

he

two

shor

test

sid

es.C

ompa

re t

he

sum

wit

h t

he

len

gth

of

the

thir

d si

de.

Wh

at c

oncl

usi

on c

an y

ou m

ake

abou

t th

ree

len

gth

s th

at d

o n

ot m

ake

atr

ian

gle?

Th

e su

m o

f th

e le

ng

ths

of

the

two

sh

ort

est

sid

es is

less

th

an o

r eq

ual

to

th

e le

ng

th o

f th

e lo

ng

est

sid

e.

9.W

hat

ru

le c

an y

ou g

ive

to t

est

any

thre

e se

gmen

t le

ngt

hs

to f

ind

out

ifth

e se

gmen

ts w

ill

form

a t

rian

gle?

Th

e su

m o

f th

e le

ng

ths

of

the

two

sh

ort

est

sid

es m

ust

be

gre

ater

th

an t

he

len

gth

of

the

thir

d s

ide.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

10

33G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–4

pygp

10-4

6MG

2.2,

6M

G2.

3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Tria

ng

les

Cha

pter

10

32G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-4

1.TA

ILO

RIN

GE

ach

lap

el o

n a

su

it ja

cket

is

in t

he

shap

e of

a t

rian

gle.

Th

e th

ree

angl

es o

f ea

ch t

rian

gle

mea

sure

47�

,68

�,an

d 65

�.C

lass

ify

the

tria

ngl

e by

its

angl

es.

acu

te

2.FL

AG

SA

nav

al d

istr

ess

sign

al f

lag

is i

nth

e sh

ape

of a

tri

angl

e.T

he

thre

e si

des

of t

he

tria

ngl

e m

easu

re 5

fee

t,9

feet

,an

d 9

feet

.Cla

ssif

y th

e tr

ian

gle

by i

tssi

des.

iso

scel

es

3.C

AR

PEN

TRY

Th

e su

ppor

ts o

f a

woo

dta

ble

are

in t

he

shap

e of

a r

igh

ttr

ian

gle.

Fin

d th

e th

ird

angl

e of

th

etr

ian

gle

if t

he

mea

sure

of

one

of t

he

angl

es i

s 23

�.67

�

4.M

APS

Th

e th

ree

tow

ns

of R

ipon

,S

part

a,an

d W

alke

r fo

rm a

tri

angl

e as

show

n b

elow

.Cla

ssif

y th

e tr

ian

gle

byit

s an

gles

an

d by

its

sid

es.W

hat

is

the

valu

e of

xin

th

e tr

ian

gle?

ob

tuse

,iso

scel

es;

38

38˚ 10

4˚˚x

Ripo

n

Spar

taW

alke

r

47 m

i30

mi

30 m

i

5.H

IKIN

GT

he

figu

re s

how

s th

e O

akC

reek

tra

il,w

hic

h i

s sh

aped

lik

e a

tria

ngl

e.C

lass

ify

the

tria

ngl

e by

its

angl

es a

nd

by i

ts s

ides

.W

hat

is

the

valu

e of

xin

th

e fi

gure

?

acu

te,s

cale

ne;

41

61˚

78˚

˚x

Rock

y Pe

ak

Mea

dow

Trai

l Hea

d

1.2

mi

0.8

mi

1.1

mi

Oak

Cree

k

6.LA

DD

ERT

he

figu

re s

how

s a

ladd

erle

anin

g ag

ain

st a

wal

l,fo

rmin

g a

tria

ngl

e.C

lass

ify

the

tria

ngl

e by

its

angl

es a

nd

by i

ts s

ides

.Wh

at i

s th

eva

lue

of x

in t

he

figu

re?

rig

ht,

scal

ene;

2466˚

˚x9

ft

4 ft

6MG

2.2,

6M

G2.

3



Use

log

ical

rea

son

ing

to s

olve

.

1.G

EOM

ETRY

Dra

w s

ever

al s

quar

es a

nd m

easu

re t

heir

int

erio

r an

gles

.Wha

tca

n yo

u co

nclu

de a

bout

the

mea

sure

s of

the

ang

les

of a

squ

are?

Did

you

use

indu

ctiv

e or

ded

ucti

ve r

easo

ning

?T

hey

are

eac

h 9

0°;i

nd

uct

ive.

2.M

ON

EYL

uke

is

inve

stin

g m

oney

in

a s

avin

gs a

ccou

nt.

Use

th

e fo

rmu

la

I�

Prt

wh

ere

Iis

th

e am

oun

t of

in

tere

st e

arn

ed,P

is t

he

prin

cipa

lam

oun

t of

mon

ey i

nve

sted

,ris

th

e in

tere

st r

ate,

and

tis

th

e le

ngt

h o

fti

me

the

mon

ey i

s in

vest

ed.I

f L

uke

in

vest

s 50

0 at

5%

in

tere

st f

or 1

yea

r,h

ow m

uch

in

tere

st w

ill

he

earn

? D

id y

ou u

se i

ndu

ctiv

e or

ded

uct

ive

reas

onin

g? $2

5;d

edu

ctiv

e

3.PA

TTER

NS

Wri

te a

ru

le t

o re

pres

ent

the

patt

ern

sh

own

bel

ow.D

id y

ou u

sein

duct

ive

or d

edu

ctiv

e re

ason

ing?

2,

4,6,

8,10

,…2n

;in

du

ctiv

e

4.ST

UD

ENT

CO

UN

CIL

Ch

en,S

ue

and

Jaco

b ar

e pr

esid

ent,

vice

pre

side

nt

and

secr

etar

y of

th

e st

ude

nt

cou

nci

l,n

ot n

eces

sari

ly i

n t

hat

ord

er.C

hen

an

dth

e vi

ce p

resi

den

t st

ayed

aft

er s

choo

l w

ith

Jac

ob t

o pl

an a

dan

ce.C

hen

is

not

th

e pr

esid

ent.

Wh

o is

th

e pr

esid

ent?

Jaco

b

5.G

EOM

ETRY

Dra

w s

ever

al p

aral

lelo

gram

s an

d m

easu

re t

hei

r si

des.

Wh

atca

n y

ou c

oncl

ude

abo

ut

the

mea

sure

s of

th

e op

posi

te s

ides

of

apa

rall

elog

ram

? D

id y

ou u

se i

ndu

ctiv

e or

ded

uct

ive

reas

onin

g?T

hey

are

co

ng

ruen

t;in

du

ctiv

e.

6.TR

AV

ELU

se t

he

form

ula

D�

rtw

her

e D

is t

he

dist

ance

,ris

th

e ra

te,a

nd

tis

th

e ti

me

to d

eter

min

e h

ow f

ar L

uci

nda

tra

vele

d if

sh

e dr

ove

65 m

iles

per

hou

r fo

r 6

hou

rs w

ith

out

stop

pin

g.D

id y

ou u

se i

ndu

ctiv

e or

ded

uct

ive

reas

onin

g?39

0 m

iles;

ded

uct

ive

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

10

35G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–5

pygp

10-5

6MR

1.2,

6M

G2.

3Sk

ills

Prac

tice

Pro

blem

-So

lvin

g In

vest

igat

ion

:Use

Lo

gic

al R

easo

nin

g

Exam

ple

Use

th

e fo

rmu

la d

�rt

wh

ere

dis

dis

tan

ce,r

is r

ate,

and

tis

ti

me

to d

eter

min

e h

ow f

ar a

car

has

tra

vele

d a

fter

4 h

ours

if

it i

s tr

avel

ing

at a

rat

e of

65

mp

h.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

10

34G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-5

Logi

cal r

easo

ning

is a

met

hod

of p

robl

em s

olvi

ng t

hat

uses

ind

uct

ive

reas

on

ing

,mak

ing

a ru

le a

fter

seei

ng s

ever

al e

xam

ples

or

ded

uct

ing

rea

son

ing

,use

a r

ule

to m

ake

a de

cisi

on.

Exp

lore

You

kn

ow t

he

car

has

tra

vele

d fo

r 4

hou

rs a

t 65

mph

.P

lan

Try

a f

ew e

xam

ples

to

fin

d a

patt

ern

.M

ake

a ta

ble.

Sol

ve

Aft

er e

ach

hou

r th

e ca

r h

as t

rave

led

65 m

ore

mil

es.

So

afte

r 4

hou

rs t

he

car

wil

l h

ave

trav

eled

260

mil

es.

Exa

min

eT

he

form

ula

is

d �

rtso

d�

65 �

4 or

260

mi.

Hou

rs P

asse

dD

ista

nce

Tra

vele

d(i

n m

iles

)1

651.

597

.52

130

2.5

162.

53

195

t65

t

Sol

ve t

he

foll

owin

g p

rob

lem

s u

sin

g lo

gica

l re

ason

ing.

1.TR

AV

ELU

se t

he

form

ula

d�

rtw

her

e d

is t

he

dist

ance

,ris

th

e ra

te,a

nd

tis

th

e ti

me

to d

eter

min

e h

ow f

ar t

he

Mor

alez

fam

ily

has

tra

vele

d if

th

eyar

e dr

ivin

g at

a r

ate

of 7

2 m

iles

per

hou

r fo

r 9

hou

rs.

648

mile

s

2.C

ELL

PHO

NES

Det

erm

ine

the

cost

per

ph

one

call

if

Mar

ia m

ade

30 c

alls

last

mon

th a

nd

her

tot

al b

ill

for

the

mon

th w

as $

45.0

0.$1

.50

per

cal

l

3.M

USI

CS

arah

,Ju

an,a

nd

Der

rick

pla

y th

e pi

ano,

tru

mpe

t,an

d vi

olin

,bu

tn

ot n

eces

sari

ly i

n t

hat

ord

er.

Sar

ah a

nd

Der

rick

sit

on

eit

her

sid

e of

th

etr

um

pet

play

er.S

arah

doe

s n

ot p

lay

the

viol

in.W

ho

play

s th

e vi

olin

?D

erri

ck

Exer

cise

s

6MR

1.2,

6M

G2.

3St

udy

Guid

e an

d In

terv

entio

nP

rob

lem

-So

lvin

g In

vest

igat

ion

:U

se L

og

ical

Rea

son

ing



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

10

37G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–5

pygp

10-5

1.PH

YSI

CS

A b

all

is d

ropp

ed f

rom

a h

eigh

tof

40

feet

.If

the

ball

bou

nce

s �1 2�

as h

igh

on e

ach

su

cces

sive

bou

nce

,wh

at i

s th

eh

eigh

t on

th

e fo

urt

h b

oun

ce?

2�1 2�

feet

2.R

ECIP

ESS

haw

n i

s m

akin

g a

cake

.He

nee

ds a

tot

al o

f 3�

1 4�cu

ps o

f fl

our.

If h

eh

as a

lrea

dy a

dded

2�1 2�

cups

,how

mu

chm

ore

does

he

nee

d to

add

?D

A2

cups

C�1 2�

cup

B1

cup

D�3 4�

cup

3.G

EOM

ETRY

Dra

w s

ever

al p

enta

gon

san

d m

easu

re t

hei

r in

teri

or a

ngl

es.

Wh

at c

an y

ou c

oncl

ude

abo

ut

the

sum

of t

he

mea

sure

s of

th

e an

gles

of

ape

nta

gon

? D

id y

ou u

se i

ndu

ctiv

e or

dedu

ctiv

e re

ason

ing?

540°

;in

du

ctiv

e

4.PA

TTER

NS

Fin

d th

e n

ext

thre

e te

rms

is t

he

sequ

ence

.2,

5,9,

14,…

20,2

7,35

5.W

OR

KT

he

tabl

e be

low

sh

ows

how

mu

ch L

u g

ot p

aid

base

d on

th

e n

um

ber

of h

ours

sh

e ba

bysa

t.P

redi

ct h

er p

ayfo

r 7

hou

rs.

$35

6.G

EOM

ETRY

Use

th

e fo

rmu

la V

�B

hw

her

e V

is t

he

volu

me

of a

cyl

inde

r,B

is t

he

area

of

the

base

an

d h

is t

he

hei

ght

of t

he

cyli

nde

r to

fin

d th

evo

lum

e of

th

e cy

lin

der

belo

w.

28 in

3

B =

3.5

in2

h =

8 in

7.FR

AM

ING

A p

hot

ogra

ph i

s 8

in.b

y 10

in

.an

d is

to

be s

urr

oun

ded

by a

mat

that

is

1.5

in.a

ll a

rou

nd.

Wh

at w

ill

beth

e di

men

sion

s of

th

e pi

ctu

re a

nd

mat

toge

ther

?11

in.b

y 13

in.

8.SC

HO

OL

Stu

den

ts f

ille

d ou

t a

surv

eyab

out

thei

r fa

vori

te s

choo

l su

bjec

ts.T

he

resu

lts

are

show

n i

n t

he

bar

grap

hbe

low

.How

man

y m

ore

stu

den

ts l

iste

dE

ngl

ish

as

thei

r fa

vori

te s

ubj

ect

than

mat

h?

10

Soci

alSt

udie

sM

ath

Engl

ish

Scie

nce

20 10 030 25 15 5

Nu

mb

er o

f h

ours

Pay

1$5

2$1

03

$15

4$2

0

6MR

1.2,

6M

G2.

3W

ord

Prob

lem

Pra

ctic

eP

robl

em-S

olv

ing

Inve

stig

atio

n:U

se L

og

ical

Rea

son

ing

Sele

ct t

he

Op

erat

ion

Mix

ed P

rob

lem

Sol

vin

g

For

Exe

rcis

es 1

an

d 2

,use

log

ical

reas

onin

g to

sol

ve t

he

pro

ble

m.

1.TO

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o yo

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sin

gle

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on a

nd

sta

te w

het

her

it

is r

egu

lar.

If i

t is

not

a p

olyg

on,e

xpla

inw

hy.

1.2.

3.

tria

ng

leN

ot

a p

oly

go

n;

it

has

a c

urv

ed s

ide.

reg

ula

r p

enta

go

n

4.5.

6.

No

t a

po

lyg

on

;it

isre

gu

lar

qu

adri

late

ral

hex

ago

nn

ot

clo

sed

.(s

qu

are)

120˚

A p

oly

go

nis

a s

impl

e, c

lose

d fig

ure

form

ed b

y th

ree

or m

ore

stra

ight

line

s.A

sim

ple

figur

e do

es n

otha

ve li

nes

that

cro

ss e

ach

othe

r.Yo

u ha

ve d

raw

n a

clos

ed f

igur

e w

hen

your

pen

cil e

nds

up w

here

itst

arte

d.P

olyg

ons

can

be c

lass

ified

by

the

num

ber

of s

ides

the

y ha

ve.

A p

olyg

on t

hat

has

all s

ides

con

grue

nt a

nd a

ll an

gles

con

grue

nt is

cal

led

a re

gu

lar

po

lyg

on

.

deca

gon

10 s

ides

nona

gon

9 si

des

octa

gon

8 si

des

hept

agon

7 si

des

hexa

gon

6 si

des

pent

agon

5 si

des

6MR

2.2

, 6A

F3.

2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

ng G

uide

Po

lyg

on

s an

d T

esse

llati

on

s

Cha

pter

10

50G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-8

Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n a

t th

e to

p o

f p

age

546

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.F

ind

the

diff

eren

ce b

etw

een

th

e sh

apes

of

the

stat

es i

n G

rou

p 1

and

the

shap

es o

f th

e st

ates

in

Gro

up

2.S

amp

le a

nsw

er:T

he

bo

rder

s o

f st

ates

in G

rou

p 1

are

str

aig

ht.

Th

e b

ord

ers

of

stat

es in

Gro

up

2 a

re n

ot

stra

igh

t.

2.W

hy

do m

ost

stat

es h

ave

bou

nda

ries

th

at a

re n

ot s

trai

ght

lin

e se

gmen

ts?

Sam

ple

an

swer

:Th

ey u

se n

atu

ral b

ou

nd

arie

s lik

e ri

vers

an

dla

kes.

Rea

d t

he

Less

on

3.H

ow m

any

stra

igh

t li

nes

can

a p

olyg

on h

ave?

thre

e o

r m

ore

4.W

hat

is

a si

mpl

e fi

gure

?S

amp

le a

nsw

er:

a fi

gu

re t

hat

do

es n

ot

hav

e lin

es t

hat

cro

ss e

ach

oth

er

5.W

hen

you

dra

w a

fig

ure

,how

can

you

tel

l w

het

her

or

not

it

is c

lose

d?S

amp

le a

nsw

er:T

he

fig

ure

is c

lose

d if

,wh

en y

ou

dra

w it

,th

ep

enci

l en

ds

up

wh

ere

it s

tart

ed.

6.H

ow d

o yo

u f

ind

the

sum

of

the

angl

e m

easu

res

in a

reg

ula

r po

lygo

n?

Sam

ple

an

swer

:D

raw

all

of

the

dia

go

nal

s fr

om

on

e ve

rtex

,co

un

t th

e n

um

ber

of

tria

ng

les

form

ed,a

nd

mu

ltip

ly b

y 18

0�.

7.In

th

is l

esso

n,t

he

term

s ve

rtex

and

vert

ices

are

use

d.H

ow a

re t

he

term

sre

late

d?S

amp

le a

nsw

er:

Ver

tice

sis

th

e p

lura

l of

vert

ex.

Rem

emb

er W

hat

Yo

u L

earn

ed8.

Usi

ng

dot

pape

r,dr

aw a

tes

sell

atio

n d

iffe

ren

t fr

om t

he

ones

sh

own

in

th

isle

sson

.You

can

use

all

th

e sa

me

shap

e or

you

can

use

com

bin

atio

ns

ofsh

apes

th

at f

orm

pat

tern

s.S

har

e yo

ur

wor

k w

ith

you

r cl

ass.

See

stu

den

ts’w

ork

.

6MR

2.2

, 6A

F3.

2



An

swer

s

Det

erm

ine

wh

eth

er e

ach

fig

ure

is

a p

olyg

on.I

f it

is,

clas

sify

th

e p

olyg

onan

d s

tate

wh

eth

er i

t is

reg

ula

r.If

it

is n

ot a

pol

ygon

,exp

lain

wh

y.

1.2.

3.

4.5.

6.

Fin

d t

he

mea

sure

of

an a

ngl

e in

eac

h p

olyg

on i

f th

e p

olyg

on i

s re

gula

r.R

oun

d t

oth

e n

eare

st t

enth

of

a d

egre

e if

nec

essa

ry.

7.do

deca

gon

8.

14-g

on9.

18-g

on10

.36

-gon

(12-

side

d)15

0°15

4.3°

160°

170°

Cla

ssif

y th

e p

olyg

ons

that

are

use

d t

o cr

eate

eac

h t

esse

llat

ion

.

11.

12.

13.

Wh

at i

s th

e pe

rim

eter

of

a re

gula

r de

cago

n w

ith

sid

es 6

.2 m

eter

s lo

ng?

62 m

14.

Fin

d th

e pe

rim

eter

of

a re

gula

r h

exag

on h

avin

g si

des

5�2 3�

inch

es l

ong.

34 in

.

KIT

ESF

or E

xerc

ises

15–

17,u

se t

he

foll

owin

g in

form

atio

n.A

kit

e m

anu

fact

ure

r m

akes

k

ites

in

th

e sh

ape

of t

he

figu

re s

how

n.

15.

Cla

ssif

y th

e sh

ape

of t

he

kite

.q

uad

rila

tera

l

16.

If �

K�

�T

and

�E

�30

°,fi

nd

m�

Kan

d m

�T

.m

�K

�m

�T

�12

0°

17.

Can

a t

esse

llat

ion

be

mad

e by

usi

ng

the

shap

e of

th

e ki

te?

Just

ify

you

r an

swer

.ye

s;36

0°is

div

isib

le b

y th

e m

easu

re o

f ea

ch a

ng

le in

th

e fi

gu

re.

KT

I E

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Po

lyg

on

s an

d T

esse

llati

on

s

Cha

pter

10

53G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–8

pygp

10-8

qu

adri

late

ral;

no

t re

gu

lar

pen

tag

on

;n

ot

reg

ula

req

uila

tera

ltr

ian

gle

;re

gu

lar

No

t a

po

lyg

on

;th

e fi

gu

re is

no

t si

mp

le.

reg

ula

r h

exag

on

No

t a

po

lyg

on

;th

e fi

gu

re

has

cu

rved

sid

es.

squ

ares

an

d

equ

ilate

ral

tria

ng

les

reg

ula

rh

exag

on

s an

deq

uila

tera

ltr

ian

gle

s

6MR

2.2

, 6A

F3.

2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eP

oly

go

ns

and

Tes

sella

tio

ns

Cha

pter

10

52G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-8

Det

erm

ine

wh

eth

er e

ach

fig

ure

is

a p

olyg

on.I

f it

is,

clas

sify

th

e p

olyg

onan

d s

tate

wh

eth

er i

t is

reg

ula

r.If

it

is n

ota

pol

ygon

,exp

lain

wh

y.

1.2.

3.

qu

adri

late

ral

No

t a

po

lyg

on

;th

ere

gu

lar

hex

ago

nfi

gu

re is

cir

cula

r.

4.5.

6.

No

t a

po

lyg

on

;th

eeq

uila

tera

l (re

gu

lar)

pen

tag

on

fig

ure

is n

ot

clo

sed

.tr

ian

gle

7.8.

9.

reg

ula

r h

epta

go

no

ctag

on

No

t a

po

lyg

on

;th

efi

gu

re is

no

t cl

ose

d.

Fin

d t

he

mea

sure

of

an a

ngl

e in

eac

h p

olyg

on.

10.

regu

lar

15-g

on15

6�11

.re

gula

r 18

-gon

160�

12.

regu

lar

24-g

on16

5�

Cla

ssif

y th

e p

olyg

ons

that

are

use

d t

o cr

eate

eac

h t

esse

llat

ion

.

13.

14.

squ

are

and

tri

ang

leh

exag

on

an

d t

rian

gle

15.

Wh

at i

s th

e pe

rim

eter

of

a re

gula

r pe

nta

gon

wit

h s

ides

8.4

in

ches

lon

g?42

in.

6MR

2.2

, 6A

F3.

2



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

10

55G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–8

pygp

10-8

Tess

ella

ted

Pat

tern

s fo

r So

lid S

hap

esT

esse

llat

ion

s m

ade

from

equ

ilat

eral

tri

angl

es c

an b

e u

sed

to b

uil

dth

ree-

dim

ensi

onal

sh

apes

.In

Exe

rcis

e 1,

you

sh

ould

get

a s

hap

e li

keth

e on

e sh

own

at

the

righ

t.It

is

call

ed a

pyr

amid

.

Cop

y ea

ch p

atte

rn.C

reas

e th

e p

atte

rn a

lon

g th

e li

nes

.T

hen

fol

low

dir

ecti

ons

for

fold

ing

the

pat

tern

.Use

tap

e to

se

cure

th

e fo

lded

par

ts.W

hen

you

hav

e fi

nis

hed

eac

h m

odel

,d

escr

ibe

it i

n w

ord

s.

1.F

old

5 ov

er 1

.R

epea

t,in

th

is o

rder

:fo

ld 6

ove

r 7,

fold

2 o

ver

6.p

yram

id w

ith

fo

ur

tria

ng

ula

r fa

ces

2.C

ut

betw

een

4 a

nd

5.T

hen

fol

d 5

over

3.

Rep

eat

in t

his

ord

er:

fold

6 o

ver

5,fo

ld 7

ove

r 12

,an

dfo

ld 2

ove

r 9.

do

ub

le p

yram

id w

ith

six

tr

ian

gu

lar

face

s

3.C

ut

betw

een

1 a

nd

2 an

d be

twee

n

14 a

nd

15.T

hen

fol

d 15

ove

r 14

.R

epea

t,in

th

is o

rder

:fo

ld 1

ove

r 2,

fold

4 o

ver

3,fo

ld 1

1 ov

er 1

,fo

ld 1

6 ov

er 5

,an

dfo

ld 1

2 ov

er 1

3.p

enta

go

nal

sh

ape

wit

h

ten

tri

ang

ula

r fa

ces

1 57

10

14

69

11

1213

15

16

2

8

34

3 810

79

12

2

4

11

56

1

1 35

24 7

6

6MR

2.2

, 6A

F3.

2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Po

lyg

on

s an

d T

esse

llati

on

s

Cha

pter

10

54G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-8

1.R

OYA

LTY

Th

e ou

tlin

e of

a c

row

n w

orn

by a

kin

g is

sh

own

bel

ow.I

s th

e fi

gure

a po

lygo

n?

If i

t is

,cla

ssif

y th

e po

lygo

nan

d st

ate

wh

eth

er i

t is

reg

ula

r.If

it

isn

ota

poly

gon

,exp

lain

wh

y.

yes;

no

nag

on

;n

ot

reg

ula

r

2.A

LCH

EMY

Th

e sy

mbo

l sh

own

is

one

of t

he

sign

s fo

r sa

lt a

lkal

iu

sed

in

17th

-cen

tury

ch

emis

try.

Is t

he

sym

bol

a po

lygo

n?

If i

t is

,cla

ssif

y th

e po

lygo

nan

d st

ate

wh

eth

er i

t is

reg

ula

r.If

it

isn

ota

poly

gon

,exp

lain

wh

y.

yes;

oct

ago

n;

no

t re

gu

lar

3.JE

WEL

RYT

he

sym

bol

show

n i

s of

ten

use

d to

rep

rese

nt

gem

s.Is

th

e sy

mbo

l a

poly

gon

? If

it

is,c

lass

ify

the

poly

gon

and

stat

e w

het

her

it

is r

egu

lar.

If i

t is

not

a po

lygo

n,e

xpla

in w

hy.

No

;th

e fi

gu

re h

as o

verl

app

ing

sid

es.

4.SY

MB

OLS

Th

e 5-

poin

ted

star

sh

own

has

side

s of

equ

al l

engt

h.I

s th

e sy

mbo

l a

poly

gon

? If

it

is,c

lass

ify

the

poly

gon

and

stat

e w

het

her

it

is r

egu

lar.

If i

t is

not

a po

lygo

n,e

xpla

in w

hy.

yes;

dec

ago

n;

no

t re

gu

lar

5.ST

AIR

ST

he

figu

re s

how

s a

side

vie

w o

fa

set

of s

tair

s.Is

th

e fi

gure

a p

olyg

on?

If i

t is

,cla

ssif

y th

e po

lygo

n a

nd

stat

ew

het

her

it

is r

egu

lar.

If i

t is

not

apo

lygo

n,e

xpla

in w

hy.

yes;

14-g

on

;n

ot

reg

ula

r

6.TE

SSEL

LATI

ON

SId

enti

fy t

he

poly

gon

sth

at a

re u

sed

to c

reat

e th

e te

ssel

lati

onsh

own

in

th

e fi

gure

.

tria

ng

le a

nd

hex

ago

n

6MR

2.2

, 6A

F3.

2



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DA

TE

___

____

____

___

PE

RIO

D

____

_

Less

on R

eadi

ng G

uide

Tran

slat

ion

s

Cha

pter

10

57G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–9

pygp

10-9

Get

Rea

dy

for

the

Less

on

Com

ple

te t

he

Min

i L

ab a

t th

e to

p o

f p

age

553

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.T

race

th

e h

oriz

onta

l an

d ve

rtic

al p

ath

bet

wee

n c

orre

spon

din

g ve

rtic

es.

Wh

at d

o yo

u n

otic

e?T

hey

hav

e th

e sa

me

pat

h,5

un

its

to t

he

rig

ht

and

2 u

nit

s d

ow

n.

2.A

dd 5

to

each

x-c

oord

inat

e of

th

e ve

rtic

es o

f th

e or

igin

al f

igu

re.T

hen

subt

ract

2 f

rom

eac

h y

-coo

rdin

ate

of t

he

vert

ices

of

the

orig

inal

fig

ure

.W

hat

do

you

not

ice?

T

he

resu

lt is

th

e co

ord

inat

es o

f th

eve

rtic

es o

f th

e fi

gu

re in

its

new

po

siti

on

.

Rea

d t

he

Less

on

3.W

hen

tra

nsl

atin

g a

figu

re,w

hat

do

you

kn

ow a

bou

t ev

ery

poin

t of

th

eor

igin

al f

igu

re?

Sam

ple

an

swer

:It

mov

es t

he

sam

e d

ista

nce

and

in t

he

sam

e d

irec

tio

n.

4.C

an a

fig

ure

be

turn

ed i

n a

tra

nsl

atio

n?

Exp

lain

.n

o;

Sam

ple

an

swer

:Wh

en a

fig

ure

is t

urn

ed,e

very

po

int

do

es n

ot

mov

e in

th

e sa

me

dir

ecti

on

.

5.W

hat

not

atio

n i

s u

sed

to i

ndi

cate

th

e ve

rtic

es o

f a

tran

slat

ed f

igu

re?

Sam

ple

an

swer

:P

rim

e sy

mb

ols

are

use

d w

ith

th

e ve

rtic

es o

fth

e tr

ansl

ated

imag

e.6.

Wh

ich

fig

ure

is

a tr

ansl

atio

n o

f F

igu

re 1

—F

igu

re 2

or

Fig

ure

3?

Exp

lain

wh

y on

e fi

gure

is

a tr

ansl

atio

n a

nd

wh

y th

e ot

her

fig

ure

is

not

a t

ran

slat

ion

.F

igu

re 3

is a

tra

nsl

atio

n o

f F

igu

re 1

;S

amp

le a

nsw

er:

Eac

h p

oin

t in

Fig

ure

1 m

oves

4 u

nit

sd

ow

n a

nd

4 u

nit

s to

th

e le

ft (

�4,

�4)

.Fig

ure

2 is

no

t a

tran

slat

ion

of

Fig

ure

1.E

ach

po

int

in F

igu

re 1

do

es n

ot

mov

e th

e sa

me

dis

tan

ce a

nd

in t

he

sam

e d

irec

tio

n t

ocr

eate

Fig

ure

2.

Rem

emb

er W

hat

Yo

u L

earn

ed7.

Des

crib

e th

e tr

ansl

atio

n g

iven

by

the

orde

red

pair

(�

7,3)

.Th

ink

of a

way

to r

emem

ber

wh

ich

dir

ecti

on t

o tr

ansl

ate

wh

en t

he

x-co

ordi

nat

e of

th

eor

dere

d pa

ir d

escr

ibin

g th

e tr

ansl

atio

n i

s n

egat

ive.

Tran

slat

e 7

un

its

left

an

d 3

un

its

up

.See

stu

den

ts’w

ork

.

1 2

3

7MG

3.2

NA

ME

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____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

TI-7

3 A

ctiv

ityIn

teri

or

An

gle

s

Cha

pter

10

56G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-8

Use

you

r ca

lcul

ator

to

expl

ore

inte

rior

ang

les

of p

olyg

ons.

The

sum

of

the

mea

sure

s of

the

inte

rior

ang

les

of a

pol

ygon

wit

h n

side

s is

:Su

m �

(n�

2) �

180°

.

If th

e po

lygo

n is

reg

ular

, the

n th

e m

easu

re o

f ea

ch in

teri

or is

this

Sum

div

ided

by

n, o

r �S

u nm �.

Use

an

d th

ese

form

ulas

to c

ompl

ete

the

tabl

e be

low

.

Step

1C

lear

all

list

s.[M

EM]6

Step

2O

pen

the

Lis

t fea

ture

.

Step

3In

L1,

ent

er n

, the

num

ber

of s

ides

.

Pre

ss

afte

r ea

ch v

alue

.

Step

4In

L2,

ent

er th

e S

um o

f In

teri

or A

ngle

s fo

rmul

a.

Hig

hlig

ht L

2.

[TEX

T]"

Don

e [S

TAT]

1 2

180

[TEX

T]"

Don

e

Step

5H

ighl

ight

L3

and

ente

r th

e fo

rmul

a fo

r th

e m

easu

re o

f ea

ch a

ngle

.

[TEX

T]"

Don

e [S

TAT]

2[S

TAT]

1

[TEX

T]"

Don

e 1.

Che

ck th

at th

e an

gle

mea

sure

s fo

r th

e oc

tago

n ar

e co

rrec

t by

eval

uatin

g th

e ex

pres

sion

sw

hen

n�

8.D

o yo

ur c

alcu

latio

ns

mat

ch th

e lis

t val

ues?

Yes,

(8 �

2) �

180

�10

80,

�10880 �

�13

5.

2.D

escr

ibe

the

tren

ds y

ou

see

in th

e su

m a

nd th

e an

gle

mea

sure

col

umns

.

Sam

ple

an

swer

:Th

e su

m v

alu

es in

crea

se b

y 18

0 as

th

e n

um

ber

of

sid

esin

crea

ses

by 1

.T

he

ang

le m

easu

re a

lso

incr

ease

s bu

t it

is a

lway

s le

ss

than

180

.

EN

TE

RE

NT

ER

2nd

2nd

2nd

2nd

EN

TE

RE

NT

ER

2nd

)2n

d(

2nd

EN

TE

R

LIS

T

EN

TE

R2n

d

LIS

T Nam

e o

f P

oly

go

nE

ach

Ang

le(R

egul

ar P

oly

go

n)

3tr

iang

le18

0°60

°

4q

uad

rila

tera

l36

0°90

°

5p

enta

go

n54

0°10

8°

6h

exag

on

720°

120°

7h

epta

go

n90

0°�

128.

57°

8o

ctag

on

1,08

0°13

5°

9n

on

ago

n1,

260°

140°

10d

ecag

on

1,44

0°14

4°

No

. of

Sid

esS

um o

f In

teri

or

Ang

les



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eTr

ansl

atio

ns

Cha

pter

10

59G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–9

pygp

10-9

1.T

ran

slat

e �

AB

C5

un

its

left

.2.

Tra

nsl

ate

rect

angl

e R

ST

U2

un

its

righ

tan

d 5

un

its

up.

3.T

ran

slat

e �

DE

F4

un

its

left

an

d 4.

Tra

nsl

ate

trap

ezoi

d L

MN

O5

un

its

righ

t4

un

its

dow

n.

and

3 u

nit

s do

wn

.

Tri

angl

e X

YZ

has

ver

tice

s X

(�4,

5),Y

(�1,

3),a

nd

Z(�

2,0)

.Fin

d t

he

vert

ices

of

XY

Z

afte

r ea

ch t

ran

slat

ion

.Th

en g

rap

h t

he

figu

re a

nd

its

tran

slat

ed i

mag

e.

5.5

un

its

dow

n6.

4 u

nit

s ri

ght,

3 u

nit

s do

wn

X(

�4,

0),

X(

0,2)

,Y

(�

1,�

2),

Y(

3,0)

,Z

(�

2,�

5)Z

(2,

�3)

Par

alle

logr

am R

ST

Uh

as v

erti

ces

R(�

1,�

3),S

(0,�

1),T

(4,�

1),a

nd

U(3

,�3)

.Fin

d t

he

vert

ices

of

RS

TU

af

ter

each

tra

nsl

atio

n.T

hen

grap

h t

he

figu

re a

nd

its

tra

nsl

ated

im

age.

7.3

un

its

left

,3 u

nit

s u

p8.

1 u

nit

rig

ht,

5 u

nit

s u

p

R(

�4,

0),

R(

0,2)

,S

(�

3,2)

,S

(1,

4),

T(

1,2)

,T

(5,

4),

U(

0,0)

U(

4,2)

y

xO

S'

R'

T'

U'

U

T

R

S

y

xO

S'

R'

T'

U'

U

T

R

S

y

xO

Y'

X'

X

Z'

Z

Y

y

xO Y'

X'

X

Z'

Z

Y

y

xOO

N

L

M

O'

N'

L'

M'

y

xO

D F

E

D'

F'

E'

y

xO

UT

RS

U'

T'

R'

S'

y

xO

B A

CB

'

A'

C'

7MG

3.2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Tran

slat

ion

s

Cha

pter

10

58G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-9

Tri

angl

e A

BC

has

ver

tice

s A

(�4,

�2)

,B(�

2,0)

,an

d C

(�1,

�3)

.F

ind

th

e ve

rtic

es o

f tr

ian

gle

AB

C

afte

r a

tran

slat

ion

of

5 u

nit

sri

ght

and

2 u

nit

s u

p.

Add

5 t

o ea

ch x

-coo

rdin

ate.

Add

2 t

o ea

ch y

-coo

rdin

ate.

Th

e co

ordi

nat

es o

f th

e ve

rtic

es o

f �

AB

C

are

A(

1,0)

,B(

3,2)

,an

d C

(4,

�1)

.

1.T

ran

slat

e �

GH

I1

un

it l

eft

and

2.T

ran

slat

e re

ctan

gle

LM

NO

4 u

nit

s ri

ght

5 u

nit

s do

wn

.an

d 3

un

its

up.

Tri

angl

e R

ST

has

ver

tice

s R

(3,2

),S

(4,�

2),a

nd

T(1

,�1)

.Fin

d t

he

vert

ices

of

RS

T

afte

r ea

ch t

ran

slat

ion

.Th

en g

rap

h t

he

figu

re a

nd

its

tran

slat

ed i

mag

e.

3.5

un

its

left

,1 u

nit

up

4.3

un

its

left

,2 u

nit

s do

wn

R(

�2,

3),S

(�

1,�

1),T

(�

4,0)

R(

0,0)

,S(

1,�

4),T

(�

2,�

3)

y

xO

S'

T'

T

R'

R

S

y

xO

S'

T'

T

R'

R S

y

xO

M'

N'

L' O'

ON

LM

y

xO

G'

I'

H'H

IG

A t

ran

slat

ion

is t

he m

ovem

ent

of a

geo

met

ric f

igur

e in

som

e di

rect

ion

with

out

turn

ing

the

figur

e.W

hen

tran

slat

ing

a fig

ure,

eve

ry p

oint

of

the

orig

inal

fig

ure

is m

oved

the

sam

e di

stan

ce a

nd in

the

sam

edi

rect

ion.

To g

raph

a t

rans

latio

n of

a f

igur

e, m

ove

each

ver

tex

of t

he f

igur

e in

the

giv

en d

irect

ion.

The

nco

nnec

t th

e ne

w v

ertic

es.

y

xO

B' C

'

A'

A

B C

Ver

tice

s of

�A

BC

V

erti

ces

of �

AB

C(x

�5,

y�

2)

A(�

4,�

2)(�

4 �

5,�

2 �

2)

B(�

2,0)

(�2

�5,

0 �

2)

C(�

1,�

3)(�

1 �

5,�

3 �

2)

A(

1,0)

B(

3,2)

C(

4,�

1)

Exam

ple

Exer

cise

s

7MG

3.2



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Tran

slat

ion

s

Cha

pter

10

61G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–9

pygp

10-9

MA

PSF

or E

xerc

ises

1–4

,use

th

e m

ap a

t th

e ri

ght.

Map

le S

t.

Blon

de S

t.

Dodg

e St

.

Paci

fic A

ve.

Cent

er R

d.

Harr

ison

St.

Kensington Ave.

Elmwood Ave.

Delaware Ave.

Main St.

New York Ave.

California Ave.

N

1.S

tan

ley’

s sc

hoo

l is

loc

ated

at

the

corn

erof

Cen

ter

and

Elm

woo

d.T

he

libr

ary

islo

cate

d at

th

e co

rner

of

Dod

ge a

nd

Del

awar

e.D

escr

ibe

Sta

nle

y’s

wal

k fr

omsc

hoo

l to

th

e li

brar

y as

an

ord

ered

pai

rof

th

e n

um

ber

of b

lock

s.(1

,2)

2.A

fter

he

goes

to

the

libr

ary,

Sta

nle

ygo

es t

o h

is A

un

t Je

ann

e’s

hou

se a

t th

eco

rner

of

Cal

ifor

nia

an

d H

arri

son

.D

escr

ibe

Sta

nle

y’s

wal

k fr

om t

he

libr

ary

to h

is a

un

t’s h

ouse

as

anor

dere

d pa

ir o

f th

e n

um

ber

of b

lock

s.(3

,�3)

3.If

a b

us

pick

s u

p pa

ssen

gers

at

the

corn

er o

f N

ew Y

ork

and

Map

le a

nd

driv

es 2

blo

cks

sou

th a

nd

3 bl

ocks

w

est,

wh

ere

does

th

e bu

s en

d u

p?th

e co

rner

of

Elm

wo

od

an

dD

od

ge

4.O

rgan

izer

s of

a w

alka

thon

wan

t to

map

out

a ro

ute

th

at w

ill

lead

peo

ple

from

the

corn

er o

f C

ente

r an

d K

ensi

ngt

on t

oth

e co

rner

of

Cal

ifor

nia

an

d M

aple

.W

rite

a c

oord

inat

e pa

ir t

hat

des

crib

esth

e m

ost

dire

ct r

oute

.(5

,4)

5.G

EOM

ETRY

Th

e fi

gure

sh

ows

anoc

tago

n p

lott

ed o

n a

coo

rdin

ate

syst

em.

Th

e fi

gure

is

to b

e tr

ansl

ated

by

5 u

nit

sle

ft a

nd

5 u

nit

s do

wn

.Gra

ph t

he

tran

slat

ed i

mag

e of

th

e fi

gure

.

y

xO

6.B

AN

KS

Cla

riss

a is

wai

tin

g in

lin

e at

th

e ba

nk.

Th

ere

are

seve

ral

peop

le i

nli

ne

in f

ron

t of

her

.Des

crib

e th

e pa

thC

lari

ssa

mu

st t

ake

to g

et t

o th

e fr

ont

of t

he

lin

e if

eac

h t

ime

she

mov

es u

p in

lin

e by

on

e po

siti

on i

s co

nsi

dere

d on

e u

nit

.

1 u

nit

rig

ht,

1 u

nit

up

,3 u

nit

s le

ft

telle

rs

Clar

issa

7MG

3.2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Tran

slat

ion

s

Cha

pter

10

60G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-9

1.T

ran

slat

e re

ctan

gle

AB

CD

3 u

nit

s ri

ght

2.T

rian

gle

PQ

Ris

tra

nsl

ated

3

and

4 u

nit

s do

wn

.Gra

ph r

ecta

ngl

e u

nit

s le

ft a

nd

3 u

nit

s do

wn

.A

BC

D.

Th

en t

he

tran

slat

ed f

igu

re i

s tr

ansl

ated

6 u

nit

s ri

ght.

Gra

ph t

he

resu

ltin

g tr

ian

gle.

Tri

angl

e E

FG

has

ver

tice

s E

(1,1

),F

(4,�

3),a

nd

G(�

2,0)

.Fin

d t

he

vert

ices

of

E�F

�G�

afte

r ea

ch t

ran

slat

ion

.Th

en g

rap

h t

he

figu

rean

d i

ts t

ran

slat

ed i

mag

e.

3.3

un

its

left

,2 u

nit

s do

wn

4.4

un

its

up

E�(

�2,

�1)

,F�

(1,�

5),G

�(�

5,�

2)

E�(

1,5)

,F�(

4,1)

,G�(

�2,

4)

5.SE

ATS

Jati

n w

as g

iven

a n

ew s

eati

ng

assi

gnm

ent

in s

cien

ce c

lass

.Th

e di

agra

m s

how

s h

is o

ld s

eat

and

his

new

sea

t.D

escr

ibe

this

tra

nsl

atio

n i

n

wor

ds a

nd

as a

n o

rder

ed p

air.

3 u

nit

s ri

gh

t,2

un

its

do

wn

;(3

,�2)

REA

SON

ING

Th

e co

ord

inat

es o

f a

poi

nt

and

its

im

age

afte

r a

tran

slat

ion

are

giv

en.D

escr

ibe

the

tran

slat

ion

in

wor

ds

and

as

anor

der

ed p

air.

6.A

(1,�

2) →

A

(3,4

) 7.

H(3

,3) →

H

(�4,

0)8.

Z(�

2,�

4) →

Z(

1,�

5)2

un

its

rig

ht

and

7

un

its

left

an

d 3

3

un

its

rig

ht

and

16

un

its

up

;(2

,6)

un

its

do

wn

;(�

7,�

3)

un

it d

ow

n;

(3,�

1)

Fro

nt o

f Cla

ssro

om

OLD

NE

W

y

xO

E'

GG'

F' F

E

y

xO

E'

G

G'

F'

F

E

y

xO

Q'

P

P'

R'

RQ

y

xO

B'

C'

DA

CB

A'

D'

7MG

3.2



Exam

ple

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Spre

adsh

eet A

ctiv

ityTr

ansl

atio

ns

Cha

pter

10

63G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–9

pygp

10-9

You

can

use

a s

prea

dshe

et t

o de

term

ine

and

grap

h th

e or

dere

d pa

irs

of a

fig

ure

afte

r a

tran

slat

ion.

Qua

drila

tera

l AB

CD

has

the

vert

ices

A(2

,3),

B(�

1,2)

,C(�

2,�

3),

and

D(3

,�1)

.Use

a s

prea

dshe

et t

o fi

nd t

he v

erti

ces

of q

uadr

ilate

ral

A'B

'C'D

'aft

er a

tra

nsla

tion

4 u

nits

left

and

2 u

nits

up.

The

n us

e th

e sp

read

shee

t to

cr

eate

a g

raph

of

AB

CD

and

A'B

'C'D

'.

Step

1U

se C

olum

n A

for

the

x-co

ordi

nate

s an

d C

olum

n B

for

the

y-co

ordi

nate

s. E

nter

the

num

bers

usi

ng th

e fo

rmul

a ba

r. T

hen

pres

s EN

TER

to m

ove

to th

e ne

xt c

ell.

Be

sure

toen

ter

the

coor

dina

tes

of th

e fi

rst p

oint

aga

in a

t the

end

of

the

list

.

Step

2In

cel

l C1,

ent

er a

n eq

uals

sig

n fo

llow

ed b

y �

A1�

4. T

hen

pres

s EN

TER

to r

etur

n th

e x-

coor

dina

te o

f th

e ne

w p

oint

.

Step

3In

cel

l D1,

ent

er a

n eq

uals

sig

n fo

llow

ed b

y �

B1�

2. T

hen

pres

s EN

TER

to r

etur

n th

e y-

coor

dina

te o

f th

e ne

w p

oint

.

Step

4To

fin

d th

e re

mai

ning

new

x-c

oord

inat

es, c

lick

on

the

bott

om r

ight

cor

ner

of c

ell C

1an

ddr

ag it

to c

ell C

5. C

lick

on

the

bott

om r

ight

cor

ner

of c

ell D

1an

d dr

ag it

to c

ell D

5to

fin

dth

e y-

coor

dina

tes.

The

coo

rdin

ates

of

A'B

'C'D

'are

A'(�

2, 5

), B

'(�5,

4),

C'(�

6, �

1), a

nd D

'(�1,

1).

Step

5To

gra

ph, h

ighl

ight

col

umns

A a

nd B

thro

ugh

row

5. P

ress

the

Cha

rt W

izar

d. S

elec

t XY

(Sca

tter

) an

d ch

oose

the

grap

h w

ith

data

poi

nts

conn

ecte

d by

line

s. P

ress

NEX

T. S

elec

tth

e S

ER

IES

tab.

Pre

ss th

e AD

Dbu

tton

. In

the

X-V

alue

s ba

r, en

ter

�Sh

eet1

!$C$

1:$C

$5. I

nth

e Y-

Val

ues

bar,

ente

r �

Shee

t1!$

D$1:

$D$5

. Pre

ss N

EXT,

NEX

T, F

INIS

Hto

dis

play

the

grap

h.

Qua

drila

tera

l QU

AD

has

vert

ices

Q(�

2,1)

,U(2

,4),

A(3

,�3)

and

D(�

1,�

1).U

sea

spre

adsh

eet

to f

ind

the

vert

ices

of

Q'U

'A'D

'aft

er a

tran

slat

ion

of 2

uni

ts r

ight

and

3 un

its

dow

n.T

hen

use

asp

read

shee

t to

gra

ph Q

UA

Dan

d Q

'U'A

'D'.

Q(

0,-2

),U

(4,

1),A

(5,

-6)

D(

1,-4

)

AB

CD

EF

GH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

2 -1 -2 3

3 2 -3 -1

-2 -5 -5 -1

5 4 -1 12

3-1

5

Sh

eet

1S

hee

t 2

Sh

eet

3

-8-6

-4-2

24

Serie

s 1

Serie

s 2

-4-3-2-10123456

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

10

62G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-9

Ch

ess

Mo

ves

In t

he

gam

e of

ch

ess,

a kn

igh

t ca

n m

ove

seve

ral

diff

eren

t w

ays.

It c

an m

ove

two

spac

es v

erti

call

y or

hor

izon

tall

y,th

en o

ne

spac

e at

a 9

0�an

gle.

It c

an a

lso

mov

e on

esp

ace

vert

ical

ly o

r h

oriz

onta

lly,

then

tw

osp

aces

at

a 90

�an

gle.

Sev

eral

exa

mpl

es

of a

kn

igh

t’s m

oves

are

in

dica

ted

on t

he

grid

at

the

righ

t.

1.U

se t

he

diag

ram

at

the

righ

t.P

lace

a k

nig

ht

or o

ther

pie

ce

in t

he

squ

are

mar

ked

1.M

ove

the

knig

ht

so t

hat

it

lan

ds o

n

each

of

the

rem

ain

ing

wh

ite

squ

ares

on

ly o

nce

.Mar

k ea

chsq

uar

e in

wh

ich

th

e kn

igh

t la

nds

wit

h 2

,th

en 3

,an

d so

on

.S

amp

le a

nsw

er g

iven

.Oth

er a

nsw

ers

are

po

ssib

le.

2.U

se t

he

diag

ram

bel

ow.P

lace

a k

nig

ht

or o

ther

pie

ce i

n t

he

squ

are

mar

ked

1.M

ove

the

knig

ht

so t

hat

it

lan

ds o

n e

ach

of

the

rem

ain

ing

squ

ares

on

ly o

nce

.Mar

k ea

ch s

quar

e in

wh

ich

th

e kn

igh

t la

nds

wit

h

2,th

en 3

,an

d so

on

.

Sam

ple

an

swer

giv

en.O

ther

answ

ers

are

po

ssib

le.

216

2717

187

22

2

15 12 3

4 23 16

8

3019

2813

2411

926

2510

514

2029 1

63

48

72

5

1

7MG

3.2



An

swer

s

Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Ref

lect

ion

s

Cha

pter

10

65G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–10

pygp

10-1

0

Det

erm

ine

wh

eth

er e

ach

fig

ure

has

lin

e sy

mm

etry

.If

so,d

raw

all

lin

es o

f sy

mm

etry

.n

o sy

mm

etry

Tri

angl

e D

EF

has

ver

tice

s D

(2,2

),E

(5,4

),an

d

F(1

,5).

Fin

d t

he

coor

din

ates

of

the

refl

ecte

dim

age.

Gra

ph

th

e fi

gure

an

d i

ts r

efle

cted

im

age

over

th

e x-

axis

.

Plo

t th

e ve

rtic

es a

nd

con

nec

t to

for

m �

DE

F.T

he

x-ax

is i

s th

e li

ne

of s

ymm

etry

.Th

e di

stan

ce f

rom

a p

oin

t on

�D

EF

to t

he

lin

e of

sym

met

ry i

s th

e sa

me

as t

he

dist

ance

fr

om t

he

lin

e of

sym

met

ry t

o th

e re

flec

ted

imag

e.T

he

imag

e co

ordi

nat

es a

re D

(2,

�2)

,E

(5,

�4)

,an

d F

(1,

�5)

.

For

Exe

rcis

es 1

an

d 2

,det

erm

ine

wh

ich

fig

ure

s h

ave

lin

e sy

mm

etry

.W

rite

yes

or n

o.If

yes

,dra

w a

ll l

ines

of

sym

met

ry.

1.2.

yes

no

3.

Tri

angl

e A

BC

has

ver

tice

s A

(0,4

),B

(2,1

),an

d C

(4,3

).F

ind

the

coor

din

ates

of

the

vert

ices

of

AB

Caf

ter

a re

flec

tion

ove

r th

e x-

axis

.Th

en g

raph

th

e fi

gure

an

d it

s re

flec

ted

imag

e.

A�(

0,�

4),B

�(2,

�1)

,an

d C

�(4,

�3)

y

xO

E'

D'D

F'

FE

A t

ype

of t

rans

form

atio

n w

here

a f

igur

e is

flip

ped

over

a li

ne o

f sy

mm

etry

is a

ref

lect

ion.T

o dr

aw t

here

flect

ion

of a

pol

ygon

, fin

d th

e di

stan

ce f

rom

eac

h ve

rtex

of

the

poly

gon

to t

he li

ne o

f sy

mm

etry

.Plo

tth

e ne

w v

ertic

es t

he s

ame

dist

ance

fro

m t

he li

ne o

f sy

mm

etry

but

on

the

othe

r si

de o

f th

e lin

e.T

hen

conn

ect

the

new

ver

tices

to

com

plet

e th

e re

flect

ed im

age.

Fig

ures

tha

t m

atch

exa

ctly

whe

n fo

lded

in h

alf

have

lin

e sy

mm

etry

.Eac

h fo

ld li

ne is

cal

led

a lin

e o

fsy

mm

etry

.Som

e fig

ures

hav

e m

ore

than

one

line

of

sym

met

ry.

y

xOA A'

BB

'

C C'

Exam

ple

s

Exam

ple

3

7MG

3.2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

ng G

uide

Ref

lect

ion

s

Cha

pter

10

64G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-1

0

Get

Rea

dy

for

the

Less

on

Com

ple

te t

he

Min

i L

ab a

t th

e to

p o

f p

age

558

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.D

escr

ibe

how

you

dre

w t

he

refl

ecti

on o

f yo

ur

clas

smat

e’s

nam

e.S

ee s

tud

ents

’wo

rk.

2.E

xpla

in w

hy

the

lin

e w

her

e th

e ge

omir

ror

and

pape

r m

eet

is c

alle

d th

eli

ne

of s

ymm

etry

.S

amp

le a

nsw

er:T

he

fig

ure

s w

ritt

en o

n t

he

pap

er a

nd

ref

lect

ed t

hro

ug

h t

he

geo

mir

ror

are

mir

ror

imag

es.

Rea

d t

he

Less

on

3.Is

th

e im

age

of a

ref

lect

ion

sm

alle

r,la

rger

,or

the

sam

e si

ze a

s th

eor

igin

al f

igu

re?

sam

e si

ze

4.In

Exa

mpl

e 4

on p

age

559,

how

can

you

tel

l th

at o

ne

imag

e is

a r

efle

ctio

nof

th

e ot

her

acr

oss

the

x-ax

is?

Sam

ple

an

swer

:If

yo

u f

old

th

eg

rid

alo

ng

th

e x-

axis

,Can

d C

w

ill b

e o

n t

op

of

each

oth

er,

as w

ill b

e B

and

B

and

Aan

d A

.5.

Stu

dy t

he

coor

din

ates

giv

en i

n E

xam

ples

4 a

nd

5 on

pag

e 55

9.H

ow c

anyo

u t

ell

how

man

y u

nit

s a

vert

ex i

s aw

ay f

rom

th

e x-

axis

wit

hou

tgr

aph

ing

it?

How

can

you

tel

l h

ow m

any

un

its

a ve

rtex

is

away

fro

m t

he

y-ax

is?

Sam

ple

an

swer

:Th

e d

ista

nce

a p

oin

t is

aw

ay f

rom

the

x-ax

is is

th

e sa

me

as t

he

y-co

ord

inat

e o

f th

e p

oin

t;th

ed

ista

nce

a p

oin

t is

aw

ay f

rom

th

e y-

axis

is t

he

sam

e as

th

ex-

coo

rdin

ate

of

the

po

int.

Rem

emb

er W

hat

Yo

u L

earn

ed6.

Wor

k w

ith

a p

artn

er.D

raw

an

d cu

t ou

t fi

gure

s of

reg

ula

r po

lygo

ns.

Dem

onst

rate

wh

ich

reg

ula

r po

lygo

ns

hav

e li

nes

of

sym

met

ry a

nd

wh

ich

do n

ot.M

ark

the

lin

es o

f sy

mm

etry

wit

h d

ash

ed l

ines

on

th

e m

odel

s.S

ee s

tud

ents

’wo

rk.

7MG

3.2



Det

erm

ine

wh

eth

er e

ach

fig

ure

has

lin

e sy

mm

etry

.If

so,c

opy

the

figu

re a

nd

dra

w a

ll l

ines

of

sym

met

ry.

1.2.

3.

no

yes

no

4.5.

6.

yes

no

yes

7.G

raph

�A

BC

wit

h v

erti

ces

A(2

,2),

8.G

raph

squ

are

AB

CD

wit

h v

erti

ces

B(5

,4),

and

C(5

,1)

and

its

refl

ecti

on o

ver

A(�

1,2)

,B(2

,�1)

,C(5

,2),

and

D(2

,5)

the

x-ax

is.T

hen

fin

d th

e co

ordi

nat

esan

d it

s re

flec

tion

ove

r th

e y-

axis

.Th

enof

th

e re

flec

ted

imag

e.fi

nd

the

coor

din

ates

of

the

refl

ecte

d im

age.

A�(

2,�

2),B

�(5,

�4)

,C�(

5,�

1)A

�(1,

2),B

�(�

2,�

1),C

�(�

5,2)

,D

�(�

2,5)

Th

e co

ord

inat

es o

f a

poi

nt

and

its

im

age

afte

r a

refl

ecti

on a

re g

iven

.D

escr

ibe

the

refl

ecti

on a

s ov

er t

he

x-ax

is o

r y-

axis

.

9.B

(1,�

2) →

B(

1,2)

10

.J

(�3,

5) →

J(

�3,

�5)

11.

W(�

7,�

4) →

W(

7,�

4)x-

axis

x-ax

isy-

axis

y

xO

D' A

A'

C

D

B'

B

C'

y

xO

C'

A A'

CB B'

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Ref

lect

ion

s

Cha

pter

10

67G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 10–10

pygp

10-1

07M

G3.

2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eR

efle

ctio

ns

Cha

pter

10

66G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


10-1

0

Det

erm

ine

wh

ich

fig

ure

s h

ave

lin

e sy

mm

etry

.Th

en d

raw

all

lin

es o

fsy

mm

etry

.

1.2.

3.

no

sym

met

ry

4.5.

6.

no

sym

met

ryG

rap

h t

he

figu

re a

nd

its

ref

lect

ion

ove

r th

e x-

axis

.Th

en f

ind

th

eco

ord

inat

es o

f th

e re

flec

ted

im

age.

7.tr

ian

gle

AB

Cw

ith

ver

tice

s A

(�3,

4),

B(1

,4),

and

C(3

,1)

A(

�3,

�4)

,B(

1,�

4),a

nd

C(

3,�

1)8.

rect

angl

e M

NO

Pw

ith

ve

rtic

es M

(�2,

�4)

,N

(�2,

�1)

,O(3

,�1)

,an

dP

(3,�

4)M

(�

2,4)

,N(

�2,

1),

O(

3,1)

,P(

3,4)

Gra

ph

th

e fi

gure

an

d i

ts r

efle

ctio

n o

ver

the

y-ax

is.T

hen

fin

d t

he

coor

din

ates

of

the

refl

ecte

d i

mag

e.

9.tr

ian

gle

DE

Fw

ith

ver

tice

s D

(1,4

),10

.tr

apez

oid

WX

YZ

wit

h v

erti

ces

W(�

1,3)

,E

(4,3

),an

d F

(2,0

)X

(�1,

�4)

,Y(�

5,�

4),a

nd

Z(�

3,3)

D(

�1,

4),E

(�

4,3)

,an

d F

(�

2,0)

W(

1,3)

,X(

1,�

4),Y

(5,

�4)

,Z(

3,3)

y

xO X

Z'

Y'

Y

ZW

W'

Z'

y

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1.2.

3.

4.5.

6.

7.8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

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how

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and.

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3.IN

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DES

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An

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6

4.A

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Chapter 10 Assessment Answer KeyQuiz 1 (Lessons 10-1 and 10-3) Quiz 3 (Lessons 10-7 and 10-8) Mid-Chapter TestPage 73 Page 74 Page 75

An

swer

s

Cop

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/McG

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of T

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w-H

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ompa

nies

, In

c.

Quiz 2 (Lessons 10-5 and 10-6)

Page 73

Quiz 4 (Lessons 10-9 and 10-10)

Page 74

1.

2.

3.

4.

5.Not a polygon; it is

not closed.

hexagon; not regular

�23

� cm

3 ft

4 in.

1.

2.

3.

4.

5.A�(3, 2); B�(1, 4);

C�(1, �1); D�(3, �3)

y

xO

B'

A'

D'

C'C

B

A

D

(�10, �4)

yes

D�(1, 5); E�(5, 5);F�(6, 2); G�(�1, 3)

(�1, 1)

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12. parallelogram

trapezoid

acute; equilateral

right; isosceles

neither

supplementary

rightobtuseacute

D

J

B1.

2.

3.

4.

5. adjacent

vertical

supplementary

complementary

sleeping

1.

2.

3.

4.

5. C

61

130

128°; obtuse

63°; acute

Chapter 10 Assessment Answer KeyVocabulary Test Form 1Page 76 Page 77 Page 78


Copyright ©

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1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Sample answer: ameasurement found byusing similar triangles tofind a dimension that is toodifficult to measure directly

Sample answer: lines in aplane that, if extendedindefinitely, will neverintersect

three

measure

obtuse

reflection

tessellation

five

four

no

complementary

angles 1.

2.

3.

4.

5.

6.

7.

8.

9.

10. G

D

J

A

G

B

H

C

G

A 11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: decagon

F

A

H

A

G

D

H

C

F

B


An

swer

s

Cop

yrig

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/McG

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c.Chapter 10 Assessment Answer Key

Form 2A Form 2BPage 79 Page 80 Page 81 Page 82

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 20-gon

H

A

G

A

G

D

H

C

G

A1.

2.

3.

4.

5.

6.

7.

8.

9.

10. H

D

G

B

F

B

F

C

F

D 1.

2.

3.

4.

5.

6.

7.

8.

9.

10. H

B

J

C

G

A

G

C

H

A 11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 16-gon

J

B

G

D

F

D

G

D

H

C


Chapter 10 Assessment Answer KeyForm 2CPage 83 Page 84

Copyright ©

Glencoe/M

cGraw


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raw-H

ill Com

panies, Inc.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. 83�

trapezoid

rectangle

90

117

82

8°

$1, 180�; $5, 30�;$10, 30�; $20, 120�;


8%$5 Bills 8%

$10 Bills

50%$1 Bills

33%$20 Bills

�JKL, �LKJ,�K, �2; obtuse

�ABC, �CBA,�B, �1; acute

straight12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

No; 160 does not gointo 360 evenly.

Avery: fish; Nathan:pasta; Alex: tacos;Takara: salad

68°

x-axis

A(1, 2), B (�2, 3),C(0, �3); A�(5, 4),B�(2, 5), C�(4, �1)

135�

108�

8 ft

No; Sample answer:

�35

� � �12

�

y

x0C'

B' A'

C

BA

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/McG

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w-H

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, In

c.


An

swer

s

Chapter 10 Assessment Answer KeyForm 2DPage 85 Page 86

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. 45�

trapezoid

rhombus

90

63

44

110°

$5, 40�; $10, 40�;$20, 160�; $100, 120�


33%$100 Bills

44%$20 Bills

11%$10 Bills

$5 Bills

11%

�QRS, �SRQ,�R, �4; acute

�FGH, �HGF, �G, �3;obtuse

right 12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

No; 135 does not gointo 360 evenly.

Avery: pasta;Nathan: fish;Alex: tacos;

Takara: salad

51°

y-axis

A�(�1, 5); B�(�4, 6);C�(�2, 0)

y

xOC'

B'

B

A'

A

C

140�

120�

5 cm

no; Sample answer:

�53

� � �31

�

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Chapter 10 Assessment Answer KeyForm 3Page 87 Page 88

1.

2.

3.

5.

6.

7.

8.

9.

10.

11. 70�

parallelogram

quadrilateral

111

53

14

71.5°


36%$1 Bills

3%$2 Bills8%

$5 Bills7%$10 Bills

23%$20 Bills

5%$50 Bills

16%$100 Bills

�CDE, �EDC, �D�6; acute

�LMN, �NML,�M, �5; obtuse

obtuse

4.

$1, 130°; $2, 12°;$5, 31°; $10, 26°;$20, 83°; $50, 18°;$100, 59°

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

Yes; 120 goesinto 360 evenly.

Avery: gymnastics;Nathan: basketball;Alex: soccer;Takara: swimming

94.8�

W�(1, 2); X �(�3, 2);Y �(�1, �1); Z �(3, �1)

y

xOZ'Y'

W'X'

Y

X

Z

W

4 units left and 3 units up

160�

144�

6 ft

No; Sample answer:�65

� � �32

�

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An

swer

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Chapter 10 Assessment Answer KeyPage 89, Extended-Response Test

Scoring Rubric

Level Specific Criteria

4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.

3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.

2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.

1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.

0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.

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Chapter 10 Assessment Answer Key Page 89, Extended-Response Test

Sample AnswersIn addition to the scoring rubric found on page A39, the following sample answers may be used as guidance in evaluating extended-response assessment items.

1. a.

The sides of a polygon are all linesegments with no curves. A polygonis simple and closed.

b. All triangles have two acute angles.Triangles are classified by theirthird angle.

See students’ triangles.

c. A rhombus is a quadrilateral thathas 4 congruent sides.

A square is a quadrilateral that has4 right angles and 4 congruent sides.

A rectangle is a quadrilateral thathas 4 right angles.

A trapezoid is a quadrilateral thathas only one pair of parallel sides.

See students’ quadrilaterals.

d. No. A trapezoid has exactly one setof parallel sides, and a rhombus hastwo sets of parallel sides.

e. A regular polygon has all sidescongruent and all angles congruent.

f. See students’ angles. Right anglesare 90�; obtuse angles are greaterthan 90� and less than 180�; straightangles are 180�, and acute angles aregreater than 0� and less than 90�.

g. The sum of two angles that aresupplementary is 180�. The sum oftwo angles that are complementaryis 90�, which is half the total forsupplementary angles, 180�.

See students’ drawings.

2. a. Octagons cannot fit together to coverspace because a third octagon cannotfit the 90� angle formed when 2octagons are placed together.

b.

See students’ explanations.

3. a. See students’ work.

b. See students’ work.


An

swer

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c.Chapter 10 Assessment Answer Key

Standardized Test PracticePage 90 Page 91

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D 11.

12.

13.

14.

15.

16.

17. A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D


Copyright ©

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raw-H

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panies, Inc.Chapter 10 Assessment Answer Key

Standardized Test PracticePage 92

18.

19.

20.

21.

22.

23.

24.

25a.

25b.

25c. (�3, 5)

Translate the figure 3units left and 5 units up.

y

xO

X'

Y'

Z

Z'

XY

trapezoid

15

� ��

5.5 6.0 6.5 7.0 7.5 8.0 8.5

��

$176.55

30

15.5%

7

Chapter 10 Resource Masters - MHSchooliv Teacher’s Guide to Using the Chapter 10 Resource Masters...

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Transcript of Chapter 10 Resource Masters - MHSchooliv Teacher’s Guide to Using the Chapter 10 Resource Masters...