Indiana Academic Standards for Geometry - McDougal … · Geometry: Concepts and Skills has been...

IndianaAcademic Standards for

Geometry

correlated to the

6/20032003

CC2

Introduction

to

Geometry: Concepts and Skills © 2003

Geometry: Concepts and Skills has been written so that all students can understand geometry.The course focuses on key topics that provide a strong foundation in the essentials of geometry.The text uses multiple representations—verbal, visual, and symbolic explanations—in everylesson. Geometry: Concepts and Skills has a clear, consistent, readable lesson format with concisegoals, clear explanations, highlighted vocabulary, visual representations and diagrams, summaryboxes, and a variety of mathematical examples. Important concepts are made understandable to allstudents through instructional diagrams, graphics and color-coding, activities, and numerousexamples throughout the textbook. The following are some of the key features.

• Concepts and Skills helps prepare students before they begin each chapter by providing aStudy Guide that focuses on important vocabulary and reviews prerequisite skills. A StudyStrategy is included, as well.

• The text develops content through examples and a variety of checkpoint exercises. Skills arerefined through homework exercises that are correlated to the examples.

• Visualize It! Notes and Exercises illustrate concepts, provide hints for remembering ideas, andask students to analyze and draw conclusions from drawings.

• Student Help notes throughout the book assist students in locating help with particularproblems; some, for example, list previous pages that have useful information or reference theMcDougal Littell Web site.

• Standardized test preparation is found in every lesson as well as at the end of every chapter.• Mixed Reviews in every lesson help students to maintain skills.• The Skills Review Handbook at the back of the student book provides explanations, examples

and practice for skills that are prerequisite to the course.

Teachers are supported by a wealth of ancillary materials. A complete listing of all programcomponents is provided on the following page.

Geometry: Concepts and Skills © 2003Components

Pupil’s EditionTeacher’s Edition

Teacher’s Resource PackageChapter Resource Books 1–11Worked Out Solution KeyPractice Workbook with Examples, Teacher’s EditionWarm-up Transparencies and Daily Homework QuizOnline Lesson Planner User’s Guide

Other AncillariesResources in SpanishMulti-Language Glossary

Transparencies: Answer Transparencies for Checking HomeworkVisualize It! Transparencies

Workbooks: Practice Workbook with Examples, Pupil’s Edition

Technology: Geometry in Motion VideoGeometry Interactive Review Games CD-ROMTest and Practice Generator CD-ROMElectronic Teacher Tools CD-ROM

PE = Pupil’s Edition, TE = Teacher’s Edition

Selected exercises are referenced in parentheses, otherwise entire page is applicable.

1

Geometry: Concepts and Skills © 2003correlated to

The Indiana Academic Standards for Geometry

INSTRUCTION APPLICATION

Pupil’s Edition andTeacher’s Edition

Print Ancillaries,Transparencies andTechnology

STANDARD 1 Points, Lines, Angles, and Planes Students find lengths and midpoints of lines. Theydescribe and use parallel and perpendicular lines. They find slopes and equations of lines.G.1.1 Find the lengthsand midpoints of linesegments in one- ortwo-dimensionalcoordinate systems.

Example: Find the length andmidpoint of the line joiningthe points A (3, 8) andB (9, 0).

PE/TE

30, 55, 194

Practice Workbook withExamples

19, 20, 21, 67, 69

Resources in Spanish

11, 22, 23, 74, 75

m c d o u g a l l i t t e l l . c o m

Sec.1.5, Homework Help;

Sec.2.1, Homework Help

PE/TE

30-33, 55-58, 194, 195, 197,198

TE Only

59

Chapter Resource Books

Ch1 : 47, 55, 70, 76; Ch2: 10,11, 13; Ch4: 37-39, 41, 43,48, 77, 79


20, 68, 69

Warm-Up Transparenciesand Daily HomeworkQuiz

6-8, 24, 25

Geometry InteractiveReview Games CD-ROM

Bike Racer

G.1.2 Constructcongruent segments andangles, angle bisectors,and parallel andperpendicular linesusing a straight edgeand compass,explaining andjustifying the processused.

Example: Construct theperpendicular bisector of agiven line segment,justifying each step of theprocess.

PE/TE

143, 144, 241, 393


52


55


Sec. 3.5, More Examples;

Sec. 3.6 Homework Help

PE/TE

148

TE Only

149


53


19

Geometry: Concepts and Skills © 2003 correlated toThe Indiana Academic Standards for Geometry



2




G.1.3 Understand anduse the relationshipsbetween special pairs ofangles formed byparallel lines andtransversals.

Example: In the diagram, thelines k and l are parallel.What is the measure of anglex? Explain your answer.

PE/TE

121, 126-131, 137-139, 146

TE Only

124, 130, 136


43, 49


50-52, 54, 60-64

Visualize It!Transparencies

14

Geometry in MotionV i d e o

3.3, 3.4, 3.5mcdouga l l i t t e l l . com:

Sec. 3.5, More Examples:

Sec. 3.6, Homework Help

PE/TE

123-125, 129, 131-135, 137,139-141, 147, 148, 162,

164- 165,

TE Only

122, 130, 138, 142


Ch3: 28, 29, 36-39, 41, 44,49, 50, 52, 58, 77-79, 81-86


46-48, 50, 51


17, 18


Flying Acrobats

G.1.4 Use coordinategeometry to findslopes, parallel lines,perpendicular lines, andequations of lines.

Example: Find an equation ofa line perpendicular toy = 4x – 2.

PE/TE

150-151, 299, 322, 665, 667

PE/TE

150-151, 299, 665, 667

1

x l

k




3




STANDARD 2 Polygons Students identify and describe polygons, and measure interior and exterior angles.They use congruence, similarity, symmetry, tessellations, and transformations. They find measures of sides,perimeters, and areas.

G.2.1 Identify anddescribe convex,concave, and regularpolygons .

Example: Draw a regularhexagon. Is it convex orconcave? Explain youranswer.

PE/TE

411, 412


Ch8: 6, 12, 13


136-138


157, 158


36


Sec. 8.1, More Examples

PE/TE

412-415, 423, 460, 461


Ch8: 4, 10, 11, 13, 17


136-138


47


Operation Clean Beach

G.2.2 Find measures ofinterior and exteriorangles of polygons,justifying the methodused.

Example: Calculate themeasure of one interior angleof a regular octagon. Explainyour method.

PE/TE

305, 311, 417-419, 615


139-141


159, 160


37


4.2, 8.2

PE/TE

418, 420-423

TE Only

419


Ch8: 18-21, 24, 27


139-141


48


157, 159-161



G.2.3 Use propertiesof congruent andsimilar polygons tosolve problems.

Example: Divide a regularhexagon into triangles byjoining the center to eachvertex. Show that thesetriangles are all the same sizeand shape, and so find thesizes of the interior angles ofthe hexagon.

PE/TE

265, 267-271, 274, 367-368


Sec. 5.5, More Examples,

Sec. 5.5 Homework Help

PE/TE

267, 279, 370, 374, 376, 377

TE Only:

263, 266, 271, 274, 280, 371,378, 387


31, 42, 4


Car Jam




4




G.2.4 Applytransformations (slides,flips, turns,expansions, andcontractions) topolygons in order todetermine congruence,similarity, symmetry,and tessellations. Knowthat images formed byslides, flips and turnsare congruent to theoriginal shape.

Example: Use a drawingprogram to create regularhexagons, regular octagons,and regular pentagons. Underthe drawings, describe whichof the polygons would bebest for tiling a rectangularfloor. Explain yourreasoning.

PE/TE

281-283, 289, 393-395, 633


Ch5: 70, 71


97-98, 133-135, 214-216

PE/TE

283, 286-289, 395-398

TE Only

290


Ch5: 65-66, 68-69, 73, 77,79;Ch7: 61, 64-67, 69, 71,73, 75-76; Ch11: 75, 78, 81,90


98

G.2.5 Find and usemeasures of sides,perimeters, and areas ofpolygons, and relatethese measures to eachother using formulas.

Example: A rectangle of area360 square yards is ten timesas long as it is wide. Find itslength and width.

PE/TE

212-215, 424-425, 430-434,438-441, 446, 447

TE Only

449





PE/TE

213, 214, 216, 217, 425, 427,428, 434-437, 442-445,

448-450

TE Only

429, 432, 433, 437, 440, 441


Ch4: 70, 72, 79; Ch8: 28-31,35, 38-41, 43, 50-53, 57,

60-63


77, 78, 142-153


41, 49-52


81-83, 162-170



G.2.6 Use coordinategeometry to proveproperties of polygonssuch as regularity,congruence, andsimilarity.

Example: Do these fourpoints form a square:(2, 1), (6, 2), (5, 6), (1, 5)?

PE/TE

153, 154, 289, 322, 399


15



PE/TE

156-158, 289, 322, 399

TE Only

159


Ch5: 71; Ch6: 30


15


6, 34




5




STANDARD 3 Quadrilaterals Students identify and describe simple quadrilaterals. They use congruence andsimilarity. They find measures of sides, perimeters, and areas.G.3.1 Describe,classify, and understandrelationships among thequadrilaterals square,rectangle, rhombus,parallelogram,trapezoid, and kite.

Example: Use a drawprogram to create a square,rectangle, rhombus,parallelogram, trapezoid, andkite. Judge which of thequadrilaterals hasperpendicular diagonals anddraw those diagonals in thefigures. Give a convincingargument that your judgmentis correct.

PE/TE

305. 309-312. 317-319. 324-327. 332-333. 337-338, 351(#37-40)


C h 6

6, 38, 43, 53, 54


102-116


116-120, 122-127


26-30


6.2 and 6.4, 6.3 and 6.4m c d o u g a l l i t t e l l . c o m

Sec. 6.1, Homework Help;

Sec. 6.3, Application Links,Bicycles; Sec. 6.4, MoreExamples; Sec. 6.4 CareerLinks, Furniture Designer;


Sec. 6.6, Career Links,

Gemologists

PE/TE

305 (#5-7), 306-308, 310(#1), 311 (#2-3), 313-315,317 (#1-3), 319 (#4-7), 320-323, 325 (#1), 326 (#2-3),328-330, 333 (#1-6), 334-336, 338 (#1-3), 339-347

TE Only

305 (#3), 308 (#3-5), 311-312, 315, 317-319, 323, 326-327, 330, 333, 336, 338, 341


Ch6: 4, 11-12, 14, 18-22, 26,29-32, 34, 37-38, 40-43, 48,51-54, 58, 60-63, 66, 68-73,78


102, 104-105, 107-108, 110-117


35-40


116-134


Shapes in Space

G.3.2 Use propertiesof congruent andsimilar quadrilaterals tosolve problemsinvolving lengths andareas.

Example: Of two similarrectangles, the second hassides three times the lengthof the first. How many timeslarger in area is the secondrectangle?

PE/TE

365-367, 371, 395-398, 401,433


Ch7: 5, 24, 25


121-123, 126


138-139



Sec. 7.2, Career Links,

Artist

PE/TE

366, 368-370, 378, 401, 404(#4, 13)

TE Only

380, 394


Ch7: 5, 22-23, 30, 37, 77


122, 123, 126


42


138, 155


Car Jam




6




G.3.3 Find and usemeasures of sides,perimeters, and areas ofquadrilaterals, andrelate these measures toeach other usingformulas.

Example: A section of roof isa trapezoid with length 4 mat the ridge and 6 m at thegutter. The shortest distancefrom ridge to gutter is 3 m.Construct a model using acomputer draw programshowing how to find the areaof this section of roof.

PE/TE

310, 312, 339, 365, 367-368,370, 424-425, 439-441, 446-447


Ch6: 21; Ch8: 30-31, 52-53,62-63


103, 109, 142-143, 148-151


162-163, 167-170




PE/TE

310, 313-315, 347 (#4, 8),

378 (#5), 425, 427-428, 440,442-445, 447-450,

TE Only

311-312, 367, 441


Ch6: 21, 22, 24, 26, 42, 58;

Ch8: 27-31, 35, 43, 50-53,57, 60-63, 65, 68


104, 109-110, 142-143, 148-141


36, 41, 48-49, 51-52


162, 166-168, 170, 173-175,177-178

Geometry InteractiveReview Games


G.3.4 Use coordinategeometry to proveproperties ofquadrilaterals such asregularity, congruence,and similarity.

Example: Do these fourpoints form a kite:(0, 0), (6, 0), (4, 2), (5, -2)?

PE/TE

322, 444


Ch6: 30

PE/TE

322, 335, 444




7




STANDARD 4 Triangles Students identify and describe types of triangles. They identify and draw altitudes,medians, and angle bisectors. They use congruence and similarity. They find measures of sides, perimeters, andareas. They apply inequality theorems.G.4.1 Identify anddescribe triangles thatare right, acute, obtuse,scalene, isosceles,equilateral, andequiangular.

Example: Use a drawprogram to create examplesof a right, acute, obtuse,scalene, isosceles, equilateral,and equiangular triangle.Identify and describe theattributes of each triangle.

PE/TE

173-175, 179-181, 185-187,191-194, 196, 199-202, 212-214, 219-223


Ch4: 4-6, 21-22, 32-33, 40-41, 53-54, 71-72


58-66, 67-72


67-70, 72-74, 77-78


16-20


4.2-4.3m c d o u g a l l i t t e l l . c o m



Sec. 4.4, Application Links,Architecture; Sec. 4.4,Homework Help; Sec. 4.7,More Examples

PE/TE

173-178, 180-184, 186,

188-190, 193-198, 202-205,213-216, 219-225

TE Only

187, 217


Ch4: 10-13, 17, 19020, 22,25, 28, 30-33, 37-41, 45, 48,51-54, 58, 69-72, 74-80, 86


69-60, 62-63, 65-66, 68, 72

Warm-UpTransparencies andDaily Homework Quiz

21-25


67-74, 76-78


Mummy Chase

G.4.2 Define, identify,and construct altitudes,medians, anglebisectors, andperpendicular bisectors.

Example: Draw severaltriangles. Construct theirangle bisectors. What do younotice?

PE/TE

206-208, 222-223, 228-229,272-275, 295


Ch4: 61-62; Ch5: 61


73-75, 96


80


4.6, 5.6



Sec. 5.6, Career Links,Facilities Planner

PE/TE

209-211, 218, 222-224, 274,276-280

TE Only

275


Ch4: 59-62, 66, 74, 77,

79-80, 86


73-75, 96


26


80, 83, 85, 87-88, 104


Mummy Chase




8




G.4.3 Constructtriangles congruent togiven triangles.

Example: Construct atriangle given the lengths oftwo sides and the measure ofthe angle between the twosides.

PE/TE

216, 241, 264

G.4.4 Use propertiesof congruent andsimilar triangles tosolve problemsinvolving lengths andareas.

Example: Of two similartriangles, the second has sideshalf the length of the first.The area of the first triangleis 20 cm2. What is the area ofthe second?

PE/TE

265-267, 279, 294, 386-389


C h 5

49-51, 81


91-93, 130, 132


101-102, 113-114, 141, 145-146, 165




PE/TE

267-271, 280, 294, 296,

388-392

TE Only

263 (#3), 387


Ch5: 53, 56


95, 131-132


31-33


103, 109-110, 141-142,

145-146

G.4.5 Prove and applytheorems involvingsegments dividedproportionally.

Example: In triangle ABC,PQ

is parallel to BC

.

What is the length of AQ

?

PE/TE

386-389


Ch7: 56-57


130-132


145-146


7.5



PE/TE

388-392

TE Only

387


Ch7: 54-57, 61, 71, 73,

75-76, 82


131-132


43, 45


145-146, 149, 1521, 153-154A

P

4

Q

12

CB

18




9




G.4.6 Prove thattriangles are congruentor similar and use theconcept ofcorresponding parts ofcongruent triangles.

Example: In the lastexample, prove that trianglesABC and APQ are similar.

PE/TE

233-235, 240-244, 250-252,257-259, 264-267, 279


Ch5: 11-13, 17, 20-21, 30-31,41-42, 50-51, 53


80-92, 94


91-102


21-24





PE/TE

234-239, 244-249, 253-256,259-263, 267-271

TE Only

242-244, 251-252, 258, 266


Ch5: 13, 18-20, 24, 27-31,36, 39-41, 44, 47-49, 56


80, 84, 86-89, 91, 93


28-32


91-100, 102

G.4.7 Find and usemeasures of sides,perimeters, and areas oftriangles, and relatethese measures to eachother using formulas.

Example: The gable end of ahouse is a triangle 20 feetlong and 13 feet high. Findits area.

PE/TE

187, 191-194, 199, 220-221,430-433, 436, 438


Ch4: 33, 40, 41; Ch8: 40


64-66, 145-147


73-75, 77-78, 164-165


18-20, 39


4.3, 4.7


Sec. 4.3, Application Link,Rock Climbing;

Sec. 8.4, Application Link,

Rock Formations

PE/TE

188-189, 193-197, 221,

224 (#7, 8), 225 (#7), 432-437

TE Only

190, 193, 198


Ch4: 33, 37-41, 45, 48, 77,79-80; Ch8: 39-41, 43, 46


65-66, 145-147


23, 27, 50


73-78, 84-87, 164-166


Mummy Chase




10




G.4.8 Prove,understand, and applythe inequalitytheorems: triangleinequality, inequalityin one triangle, andhinge theorem.

Example: Can you draw atriangle with sides of length7 cm, 4 cm, and 15 cm?

PE/TE

212-214, 216, 223


Ch4: 71-72


76-78


82



PE/TE

213-218, 223, 224 (#15),

225 (#3)


Ch4: 69-72, 74


76-78


82


Mummy Chase

G.4.9 Use coordinategeometry to proveproperties of trianglessuch as regularity,congruence, andsimilarity.

Example: Draw a trianglewith vertices at (1, 3),(2, 5), and (6, 1). Drawanother triangle with verticesat (-3, -1), (-2, 1), and (2, -3).Are these triangles the sameshape and size?

PE/TE

289, 399


98


106

PE/TE

155, 289

TE Only

193


Ch5: 71


98


106




11




STANDARD 5 Right Triangles Students prove the Pythagorean Theorem and use it to solve problems. Theydefine and apply the trigonometric relations sine, cosine, and tangent.G.5.1 Prove and usethe PythagoreanTheorem.

Example: On each side of aright triangle, draw a squarewith that side of the triangleas one side of the square.Find the areas of the threesquares. What relationship isthere between the areas?

PE/TE

191-194, 199-202, 436,

491-492, 494, 512, 542, 549,570-571, 627-628


Ch4: 39, 41, 53-54;Ch9:

32-33; Ch10: 60-61


67-68, 70-72, 163-164, 176


74-75, 77-78, 185-186


44-46


Sec. 4.4, Application Link,Petronas Towers;




PE/TE

193-198, 202-205, 436-437,493-499, 512-516, 572-575,579-580

TE Only

201, 492, 570-571


Ch4: 38-41, 45, 48, 51-54,58, 77, 79; Ch9: 30-33, 38,46, 68; Ch10: 60-61


68, 71-72, 164, 176


24-25, 56, 60


74-78, 185-186

G.5.2 State and applythe relationships thatexist when the altitudeis drawn to thehypotenuse of a righttriangle.

Example: In triangle ABCwith right angle at C, draw

the altitude CD

from C toAB

. Name all similartriangles in the diagram. Usethese similar triangles toprove the PythagoreanTheorem.

Prerequisite and related skillsare taught on the followingpages:

PE/TE

357-360, 386-389

Prerequisite and related skillsare taught on the followingpages:

PE/TE

361-364, 390-392




12




G.5.3 Use special righttriangles (30° - 60° and45° - 45°) to solveproblems.

Example: An isosceles righttriangle has one short side of6 cm. Find the lengths of theother two sides.

PE/TE

542-544, 548-551, 554


21-22, 29-30


178-183


204-207


49-50




PE/TE

543-546, 550-555

TE Only

547


Ch10: 19-22, 26-30, 36


178-183


61-62


204-207, 216, 218

G.5.4 Define and usethe trigonometricfunctions (sine, cosine,tangent, cosecant,secant, cotangent) interms of angles of righttriangles.

Example: In triangle ABC,tan A = 1/5Find sin A and cot A.

PE/TE

556-559, 563-565, 569-571,578-579


Ch10: 6, 42-43, 51-52, 60-61


184-188, 190-192


209-214


49-50


Sec. 10.4, Career Link,Foresters;



PE/TE

558, 560-562, 564-568, 570,572-575, 578-581

TE Only

559, 571


Ch10: 33, 40-43, 47, 49-50,52, 57-61


184-189, 191-192


64-65


205-215, 217, 219-220

G.5.5 Know and usethe relationships in 2 x + cos2 x = 1.

Example: Show that, in aright triangle,sin2 x + cos2 x = 1 is anexample of the PythagoreanTheorem.

Opportunities to address thisstandard can be found on thefollowing pages:

PE/TE

556-559, 563-565, 569-572


PE/TE

560-562, 566-568, 572-575




13




G.5.6 Solve wordproblems involvingright triangles.

Example: The force ofgravity pulling an objectdown a hill is its weightmultiplied by the sine of theangle of elevation of the hill.What is the force on a 3,000-pound car on a hill with a 1in 5 grade? (A grade of 1 in 5means that the hill rises oneunit for every 5 horizontalunits.)

PE/TE

559

PE/TE

553-554, 561-562, 573-574

580-581

TE Only

559, 568


Ch10: 10-11, 19, 28, 41, 49-50, 57-59




14




STANDARD 6 Circles Students define ideas related to circles: e.g., radius, tangent. They find measures ofangles, lengths, and areas. They prove theorems about circles. They find equations of circles.G.6.1 Find the centerof a given circle.Construct the circlethat passes throughthree given points (notin a straight line).

Example: Given a circle, findits center by drawing theperpendicular bisectors of twochords.

PE/TE

609, 612, 618m c d o u g a l l i t t e l l . c o m

Sec. 11.4, Career Link,Archaeologists;

Sec. 11.4, Career Link,

EMTs

TE Only

609

G.6.2 Define andidentify relationshipsamong: radius,diameter, arc, measureof an arc, chord, secant,and tangent.

Example: What is the anglebetween a tangent to a circleand the radius at the pointwhere the tangent meets thecircle?

PE/TE

589-590, 594-597, 601-603,608-610, 613-616, 620-622

TE Only:

626-629


Ch11: 1-2, 20-21, 29-30, 39-40, 47-48, 58-59


196-199, 201-210


225-228, 230-235


51-53






PE/TE

590-593, 597-600, 603-607,610-612, 615-619, 621-625,627, 629-632

TE Only

596, 602, 609, 628


Ch11: 18-21, 26-30, 36-40,44-48, 52, 56-59, 61, 64


197-198, 200-201, 203-204,206-210


67-71


225-235


Pinball Express

G.6.3 Prove theoremsrelated to circles.

Example: Prove that theangle subtended by a chord atthe center of a circle is twicethe angle at thecircumference.


PE/TE

595, 597, 608, 609, 613, 614,615, 616, 620, 622




15




G.6.4 Constructtangents to circles, andcircumscribe andinscribe circles.

Example: Draw an acutetriangle and construct thecircumscribed circle.


PE/TE

615-616


PE/TE

619 (#35-38)

G.6.5 Define, find, anduse measures of arcsand related angles(central, inscribed, andintersections of secantsand tangents).

Example: Find the measureof angle ABC in the diagrambelow.

PE/TE

601, 613-616, 620-622, 626


Ch11: 40, 47-48, 58-59


199-209


227-228, 232-235


52-53




PE/TE

603-604, 616-619, 621-625

TE Only

602, 615


Ch11: 4, 27, 40, 44-48, 52,56-57, 59, 61, 64


199-209


68-70


227-228, 232-236


Pinball Express

G.6.6 Define andidentify congruent andconcentric circles.

Example: Are circles with thesame center always the sameshape? Are they always thesame size?

PE/TE

602

B

C

A

15




16




G.6.7 Define, find, anduse measures ofcircumference, arclength, and areas ofcircles and sectors. Usethese measures to solveproblems.

Example: Which will giveyou more: three6-inch pizzas or two8-inch pizzas?Explain your answer.

PE/TE

451-454, 463, 603


Ch11: 30, 47, 71-72


154-156


171-172

PE/TE

453-459, 463-465,

516 (#46-48), 603, 606


Ch11: 28, 30, 69-72, 75,

82-83


154-156


53


171-172, 175 (#22-24),

177 (#25-26), 178 (#10)

G.6.8 Find theequation of a circle inthe coordinate plane interms of its center andradius.

Example: Find the equationof the circle with radius 10and center (6, -3).

PE/TE

627-629, 631m c d o u g a l l i t t e l l . c o m

Sec. 11.7, Homework Help


Ch11: 69-70


211-213


237-238


54

PE/TE

627, 629-632

TE Only

628


Ch11: 67-70, 75


211-213


72


237-238


Pinball Express




17




STANDARD 7 Polyhedra and Other Solids Students describe and make polyhedra and other solids. Theydescribe relationships and symmetries, and use congruence and similarity.G.7.1 Describe andmake regular and non-regular polyhedra.

Example: Is a cube a regularpolyhedron? Explain why orwhy not.

PE/TE

473-475, 508


Ch9: 5-6, 13


157-158


181-182


41-42

PE/TE

476-480

TE Only

474


Ch9: 10-11, 13


157-158


54


181-182

G.7.2 Describe thepolyhedron that can bemade from a given net(or pattern). Describethe net for a givenpolyhedron.

Example: Make a net for atetrahedron out of posterboard and fold it up to makethe tetrahedron.

PE/TE

481, 483-484


Ch9: 19-20


160


183


43

PE/TE

497

TE Only

484, 489


Ch9: 19


161

G.7.3 Describerelationships betweenthe faces, edges, andvertices of polyhedra.

Example: Count the sides,edges, and corners of a square-based pyramid. How are thesenumbers related?

PE/TE

479


Ch9: 13


159


182

PE/TE

479


Ch9: 11, 13


159


182




18




G.7.4 Describesymmetries ofgeometric solids.

Example: Describe therotation and reflectionsymmetries of a square-basedpyramid.


PE/TE

473-475


PE/TE

476-480

G.7.5 Describe sets ofpoints on spheres:chords, tangents, andgreat circles.

Example: On Earth, is theequator a great circle?


PE/TE

517-519

TE Only

470D


PE/TE

519-522

G.7.6 Identify andknow properties ofcongruent and similarsol ids .

Example: Explain how thesurface area and volume ofsimilar cylinders are related.

Teachers may extend thelessons on the following pagesto address this standard:

PE/TE

483-486, 491-494, 500-502,510-512

Teachers may extend thelessons on the following pagesto address this standard:

PE/TE

487-490, 495-499, 503-507,513-516

TE Only

470D

G . 7 . 7 Find and usemeasures of sides,volumes of solids, andsurface areas of solids,and relate thesemeasures to each otherusing formulas.

Example: An ice cube isdropped into a glass that isroughly a right cylinder witha 6 cm diameter. The waterlevel rises 1 mm. What is thevolume of the ice cube?

PE/TE

481-486, 492-494, 500-502,508-512, 517-519, 525-527


Ch9: 21, 27, 32-33, 41, 49,59-60


160-167, 169-171


183-186, 188, 190-193


43-45




Sec. 9.6, Application Link,

Astronomers

PE/TE

486-490, 494-499, 501-507,511-516, 518-523, 525-529

TE Only

484, 492


Ch9: 18-21, 26, 30-33, 35,38-42, 46-50, 55, 57-60, 62,66-70


160-162, 165-167, 169-171


55-59


183-199


Clown House




19




STANDARD 8 Mathematical Reasoning and Problem Solving Students use a variety of strategies tosolve problems.G.8.1 Use a variety ofproblem-solvingstrategies, such asdrawing a diagram,making a chart, guess-and-check, solving asimpler problem,writing an equation,and working backwards.

Example: How far does thetip of the minute hand of aclock move in 20 minutes ifthe tip is 4 inches from thecenter of the clock?

PE/TE

3-4, 8-9, 43, 653-654


Ch1: 12-13, 19, 21


1-5


1-3

PE/TE

3-7, 9-13, 43


Ch1: 10, 12-13, 18, 20-22,26, 66, 68, 70-72


2-5


1-3

G.8.2 Decide whether asolution is reasonablein the context of theoriginal situation.

Example: John says theanswer to the problem in thefirst example is “12 inches.”Is his answer reasonable?Why or why not?

See "Error Analysis":

PE/TE

12, 33, 93, 118, 134, 176,210, 216, 239, 248, 276, 321,369, 443, 456, 477, 489, 496,514, 520, 546, 561, 566, 632

Students develop and evaluate mathematical arguments and proofs.

G.8.3 Makeconjectures aboutgeometric ideas.Distinguish betweeninformation thatsupports a conjectureand proof of aconjecture.

Example: Calculate the ratiosof side lengths in severaldifferent-sized triangles withangles of 90°, 50° and 40°.What do you notice about theratios? How might you provethat your observation is true(or show that it is false)?

PE/TE

10, 127, 191, 199, 206, 272,364, 416, 482, 521, 548


4-5


3

PE/TE

10, 12-13, 43, 46

TE Only

10


4-5


3


3




20




G.8.4 Write andinterpret statements ofthe form “if – then” and“if and only if.”

Example: Decide whether thisstatement is true: “If today isSunday, then we have schooltomorrow.”

PE/TE

82-84, 97


Ch2: 50-51


31-33


31-32



PE/TE

83-87, 97


Ch2: 48-51, 55, 70 (#21-23)


31-33


17


31-32

G.8.5 State, use, andexamine the validity ofthe converse, inverse,and contrapositive of“if – then” statements.

Example: In the lastexample, write the converseof the statement.

PE/TE

136-139


Ch3: 51


49-50


53



PE/TE

137


Ch3: 49-51


50


53

G.8.6 Identify and giveexamples of undefinedterms, axioms, andtheorems, and inductiveand deductive proof.

Example: Do you proveaxioms from theorems ortheorems from axioms?

PE/TE

8, 14, 69, 83


Ch1: 31


4, 7, 25, 31


5, 31

PE/TE

84, 86

G.8.7 Constructlogical arguments,judge their validity, andgive counterexamplesto disprove statements.

Example: Find an example toshow that triangles with twosides and one angle equal arenot necessarily congruent.

PE/TE

10


Ch1: 22


32-33m c d o u g a l l i t t e l l . c o m


PE/TE

10, 12-13, 84, 86


Ch1: 22, 26, 66, 68, 70


33




21




G.8.8 Write geometricproofs, includingproofs by contradictionand proofs involvingcoordinate geometry.Use and compare avariety of ways topresent deductiveproofs, such as flowchart, paragraph, two-column, and indirect.

Example: In triangle LMN,LM = LN.

Prove that ∠LMN ≅ ∠LNM.

PE/TE

243-244, 252, 267


84, 90-92


94, 99, 101-102




PE/TE

244, 247-248, 256, 259, 262,265, 267, 269-270

TE Only

253, 258, 266


84, 90-93


94, 99, 101-102

G.8.9 Perform basicconstructions,describing andjustifying theprocedures used.Distinguish betweenconstructing anddrawing geometricfigures.

Example: Construct a lineparallel to a given linethrough a given point not onthe line, explaining andjustifying each step.

PE/TE

144, 187, 216 (Example)

PE/TE

143, 144, 148 (#22-24), 216(#34-36), 241, 321 (#23),393, 594

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