10th Grade Honors Geometry - Findlay City · PDF file16 6 Circle Properties...

10th Grade

Honors Geometry (Course #241)

Course of Study

Findlay City Schools 2006

Table of Contents

1. Findlay City Schools Mission Statement & Beliefs 2. Honors Geometry Curriculum Map 3. Honors Geometry Indicators

Course of Study Writing Team

Todd Boblitt

Karen Ouwenga

Mission Statement

The mission of the Findlay City Schools, a community partnership committed to educational excellence, is to instill in each student the knowledge, skills and virtues necessary to be lifelong learners who recognize their unique talents and purpose and use them in pursuit of their dreams and for service to a global society. This is accomplished through a passion for knowledge, discovery and vision shared by students, families, staff and community.

Beliefs Our beliefs form the ethical foundation of the Findlay City Schools. We believe….

• every person has worth • every individual can learn • family is the most important influence on the development

of personal values. • attitude is a choice and always affects performance • motivation and effort are necessary to achieve full

potential • honesty and integrity are essential for building trust. • people are responsible for the choices they make. • performance is directly related to expectations. • educated citizens are essential for the survival of the

democratic process. • personal fulfillment requires the nurturing of mind, body

and spirit. • every individual has a moral and ethical obligation to

contribute to the well-being of society. • education is a responsibility shared by students, family,

staff and community. • the entire community benefits by investing its time,

resources and effort in educational excellence. • a consistent practice of shared morals and ethics is

essential for our community to thrive.

HONORS GEOMETRY CURRICULUM MAP

WEEK CHAPTER TOPIC INDICATORS

1 1 Points, Lines, Planes & Angles

10.11


10.11


10.11

4 2 Reasoning & Proof 10.12 5 2 Reasoning & Proof 10.12 6 2 Reasoning & Proof 10.12 7 3 Parallel & Perpendicular

lines 10.28;10.29;10.30;9.21

8 3 Parallel & Perpendicular lines

10.28;10.29;10.30;9.21

9 3 Parallel & Perpendicular lines

10.28;10.29;10.30;9.21

10 4 Congruent Triangles 10.1;10.12;10.15;10.16 11 4 Congruent Triangles 10.1;10.12;10.15;10.16 12 4 Congruent Triangles 10.1;10.12;10.15;10.16 13 5 Polygon Properties 10.1;10.10;10.12 14 5 Polygon Properties 10.1;10.10;10.12;10.13;10.14 15 6 Circle Properties 10.10;10.9;10.19;10.27 16 6 Circle Properties 10.10;10.9;10.19;10.27 17 Ch. 6 &

Exam Review Circle Properties & EXAM REVIEW

10.10;10.9;10.19;10.27

18 EXAMS – 1st SEMESTER 19 7 Transformations &

Tesselations 10.15;10.16

20

7 Transformations & Tesselations

10.15;10.16

21 7 Translations & Tesselations 10.15;10.16 22 8 Area 10.22;10.29 23 8 Area 10,22;10.29 24 8 Area 10.22;10.19 25 9 Pythagorean Theorem 10.12 26 OGT REVIEW &

Pythagorean Theorem 10.12

27 OGT TEST & Pythagorean Theorem

10.12

28 10 Volume 9.8;9.10 29 10 Volume 9.8;9.10 30 11 Similarity 10.12;9.8

31 11 Similarity 10.12;9.8 32 12 Trigonometry 10.12 33 12 Trigonometry 10.12 34 13 Geometry as a Mathematical

System 9.1;9.8;10.12

35 Ch 13 & Exam Review

Geometry as a Mathematical System

9.1;9.8;10.12

36 EXAMS - FINALS

BENCHMARK: (A) Formally define geometric figures STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 1 Time Line: Indicator: #10.11 (Characteristics and Properties) Recognize and explain the necessity for certain terms to remain undefined, such as point, line and plane.

KNOW

• Learn to identify and draw models of points, lines and planes, and determine their characteristics.

• Become familiar with the objects that have special characteristics: acute and obtuse angles and triangles; scalene triangles, collinear points, coplanar figures, congruent figures, equilateral, equiangular and regular polygons.

Begin defining parts of geometric objects: center, radius, chard and diameter of a circle; cross section of a three-dimensional solid

DO

• Be able to draw representations of points, lines and planes.

• Be able to write and recognize the symbols showing points, lines and planes.

• Be able to write the

postulate that justifies the examples using points, lines and planes.

Translate descriptions into diagrams and vise versa Encounter some real-world applications of geometry Develop critical thinking Develop construction skills Develop the skills of measuring angles and line segments, marking figures and writing and recording definitions

PRE-ASSESSMENT:

ASSESSMENT: Chapter 1 Test Quiz 1 (Lessons 1.1-1.3) Quiz 2 (Lessons 1.4-1.5) Quiz 3 (Lessons 1.6-1.8) Chapter 1 Constructive Assessment Options

GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Week 1 and Week 2 of Countdown to OGT pp. OH8 and OH9 in textbook. Textbook: pp. 58-59, Preparing for Standardized Test

BEST PRACTICES: Patty Paper Discovering Geometry with Geometer’s Sketchpad

RESOURCES: Textbook Workbook Teaching and Worksheet Masters Sketchpad Physical Objects (spaghetti, tack, modeling clay, cardboard, stiff wire)

TESTING VOCABULARY: Organizing a notebook pg. 92

HISTORICAL/MODERN LINK: M.C. Escher pg. 27 Poolroom Math pg. 38-41 Fermat pg. 74 Geometric Probability pg. 86-87

BENCHMARK: (H) Establish the validity of conjectures about geometric objects; their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 2 Time Line: 10 days Indicator: #9.1 Identify and justify whether properties (properties of algebra) #10.12 Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.

KNOW

• Learn the components of a conditional statement

• Learn to use the properties of algebra to justify statements.

• Learn special angle relationships

• Learn to identify perpendicular lines and their properties

DO

• Be able to identify the hypothesis and the conclusion of a conditional statement.

• Be able to correctly state the algebraic property used justifying each step of an algebraic or geometric proof.

• Be able to recognize and use

the characteristics of complementary supplementary, and vertical angles.

• Be able to recognize and use

perpendicular lines.

PRE-ASSESSMENT: Practice Your Skills for Chapter 1

ASSESSMENT: Versions A and B of:

Quiz 1, 2 and 3 Chapter 2 Test Chapter 2 Constructive Assessment

GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad (Ch 2.2, 2.3, 2.5 and 2.6)

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Week 3 and Week 4 of Countdown to OGT pp. OH10-12 from textbook. Standardized Test Practice.

BEST PRACTICES: Cooperative Learning Journal writing p. 140

RESOURCES: Textbook Workbook Practice Masters Construction Tools Sketchpad

TESTING VOCABULARY: Organizing a notebook

HISTORICAL/MODERN LINK: Language Connection p. 94 Science Connection p. 101, 117 An Introduction tot he History of Mathematics by Howard Eves. (Resources)

BENCHMARK: C) Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines. STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 3 Time Line: 15 days Indicator: #10.28 (Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals) #9.21 (Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to given through a specific point)

KNOW

• Learn to identify the angles formed by two lines intersected by a transversal.

• Identify the angles formed and use

their characteristics when two parallel lines are cut by a transversal.

• Find the slope of parallel and

perpendicular lines • Write an equation of a line given

information about its graph

• Solve problems by writing equations

DO

• Be able to name the angles formed by two lines intersected by a transversal

• Be able to identify alternate interior angles, corresponding angles, and same side interior angles and use their characteristics to find the measures of missing angles.

• Be able to find the slope

of parallel and perpendicular lines.

• Be able to write an

equation of a line given the slope.

• Be able to write an equation of a line given two points, the slope and a point, and a point and the y intercept.

PRE-ASSESSMENT: Practice Your Skills for Chapter 2 (resources)

ASSESSMENT: Assessment A and B for:

Quiz 1, 2 and 3 Ch 3 Test Ch 3 Constructive Assessment Chapters 1-3 Exam

GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad (Ch 3.2 – 3.4, 3.7 and 3.8)

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Week 5 and Week 6 of Countdown to OGT pp. OH12 and OH13 in textbook

BEST PRACTICES: Cooperative Learning Journal writing p. 196 Exploration

RESOURCES: Textbook Workbook Practice Masters Construction Tools Sketchpad Graph Paper


HISTORICAL/MODERN LINK: Perspective Drawing (Art Link) p. 172-175 Art Connection p. 180 Science Connection p. 185

BENCHMARK: (B) Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence. STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 4 Time Line: 14 days Indicator: #10.12 (b,c) (Characteristics and Properties) Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including: (b) prove theorems involving triangle similarity and congruence (c) prove theorems involving properties of lines, angles, triangles and quadrilateral. #10.13 (Spatial Relationships). Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software. #10.14 (Spatial Relationships) Construct congruent figures and similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software.

KNOW

• Identify and classify triangles by angles.

• Identify and classify triangles by sides.

• Learn the theorems related to angles of a triangle.

• Identify the corresponding

parts of congruent triangles.

• Learn the methods used to prove two triangles are congruent.

DO

• Be able to identify the triangle as acute, obtuse, right, or equiangular

• Be able to identify the triangle

as scalene, isosceles, or equilateral

• Be able to apply the angle sum

and exterior angle theorems.

• Be able to list all corresponding parts of congruent triangles.

• Be able to identify the specific

method (SSS, SAS, ASA, and AAS) used to prove two

• Using constructions to prove triangle congruence

triangles are congruent. • Be able to use the specific

methods of triangle congruence in prove form.

• Use basic constructions

involving angles and sides to prove triangle congruency.



Quiz 1, 2 and 3 Chapter 4 Test

Chapter 4 Constructive Assessment

GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad (Ch 4.1 – 4.5, 4.8)





HISTORICAL/MODERN LINK: Recreation Connection p.217 Career Connection p. 220 Architecture connection p. 198, 204 History Connection p. 245

BENCHMARK: (E) Draw and construct representations of two-and-three-dimensional geometric object using a variety of tools, such as straightedge, compass and technology. (H) Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others. STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 5 Time Line: 12 days Indicator: #10.10(a) Formally define and explain keys aspects of geometric figures, including: (a) interior and exterior angles of polygons. #10.12(c) Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including (c) prove theorems involving properties of lines, angles, triangles and quadrilaterals: (d) test a conjecture using basic constructions made with a compass and straightedge or technology. #10.13 (Spatial Relationships) Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software. #10.14 (Spatial Relationships) Construct congruent figures and similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software. #10.23 Use algebraic representations and functions to describe and generalize geometric properties and relationships.

KNOW

• Find the sum of the measures of the interior angles of a polygon.

• Find the sum of the measures of the exterior angles of a polygon.

• Recognize and apply properties

of the sides and angles of parallelograms.

• Recognize and apply properties of the diagonals of parallelograms.

DO

• Have students figure interior and exterior angle sum for any polygon.

• Solve problems involving the properties of a parallelogram.

• Recognize the conditions that

ensure a quadrilateral is a parallelogram.

• Prove that a set of points forms a parallelogram in the coordinate plane.

• Recognize and apply properties of rectangles.

• Determine whether parallelogram and rectangles.

• Recognize and apply the properties of rhombi.

• Recognize and apply the properties of squares.

• Recognize and apply the

properties of trapezoids. • Solve problems involving the

medians of trapezoids.

• Position and label quadrilateral for use in coordinate proofs.

• Prove theorems using coordinate proofs.

• Have students recognize and

prove when a quadrilateral is a parallelogram.

• Have students identify and solve problems involving special quadrilaterals.

• Have students solve problems involving the properties of trapezoids.

• Have students use the distance formula in associated problems involving the special quadrilaterals.




GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad (Ch 5.1 – 5.6) .





HISTORICAL/MODERN LINK: Architecture Connection p. 271 Career Connection p. 289

BENCHMARK: (C ) Apply indirect measurement techniques, tools and formulas, as appropriate to find perimeter, circumference and area of circles, triangles,quadrilaterals and composite shapes, and to find volume of prisms,cylinders, and pyramids. STANDARD: Measurement TOPIC/UNIT: Chapter 6 Time Line: 15 days Indicator: #10.9 Determine the measures of central and inscribed angles and their associated major and minor arcs. #10.10 (d) Formally define and explain key aspects of geometric figures, including circles (radius, diameter chord, circumference, major arc, minor arc, sector, segment, inscribed angle). #10.19 Solve problems involving chords, radii and arch within the same circle. #10.27 Graph the quadratic relationship that define circles.

KNOW

• Identify and use parts of circles • Solve problems involving the

circumference of a circle • Recognize major arcs, minor

arcs, semicircles, and central angles and their measures.

• Find arc length. • Recognize and use relationships

between arcs and chords. • Recognize and use relationships

between chords and diameters. • Find the measures of inscribed

angles. • Find measures of angles of

inscribed polygons. • Use properties of tangents.

DO

• Solve problems involving arc length, circumference, and measures of angles in circles.

• Solve problems involving chords and diameters of circles.

• Students will solve problems involving inscribed angles of circles and polygons.

• Solve problems involving circumscribed polygons.

• Find measures of angles formed by lines intersecting on or inside a circle.

• Find measures of angles formed by lines outside the circle.

• Find the measures of segments that intersect in the interior of a circle.

• Find measures of segments that intersect in the exterior of a circle.

• Write the equation of a circle. • Graph a circle on the coordinate

plane.

• Students will use properties of tangents to solve problems involving tangents in a circle.

• Find the measures of the angles formed by lines intersecting on, inside, or outside of a circle.

• Find the measures of an arc

length, tangent segment, or chord of a circle.

• Write the equation of a circle and be able to graph the circle on a coordinate plane.



Quiz 1, 2 and 3 Chapter 6 Test Chapter 6 Constructive Assessment Chapters 4-6 Exam

GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad (Ch 6.1 – 6.3 and 6.5)





HISTORICAL/MODERN LINK: History Connection p. 331 Science Connection p. 334 Cultural Connection p. 341 Art Connection p. 345 Geography Connection p. 351

BENCHMARK: (F) Represent and model transformations in a coordinate plane and describe the results STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 7 Time Line: 13 days Indicator: #10.15 (Transformation and Symmetry). Identify the reflection and rotation symmetries of two-and-three dimensional figures. #10.16 (Transformation and Symmetry) Perform reflections and rotations.

KNOW

• Name, draw and recognize figures that have been reflected, translated, rotated, or dilated.

DO

• Students will draw reflected, translated, and rotated images in the coordinate system.

• Students will recognize and draw lines

of symmetry and points of symmetry.

• Students will determine the scale factor for a given dilation.

• Students will determine whether a

dilation is an enlargement, a reductions, or a congruence transformation.





GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad (Ch 7.1 – 7.8)





HISTORICAL/MODERN LINK: Art Connection p. 362 Mathematics Connections p. 381, 385 Cultural Connection p. 386 Career Connection p. 407

BENCHMARK: (C ) Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangles, quadrilaterals and composite shapes, and to find volume of prisms, cylinders, and pyramids; (E) Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision. STANDARD: Measurement TOPIC/UNIT: Chapter 8 Time Line: 14 days Indicator: #10.22 Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height. #10.29 Solve real-world problems that can be modeled using linear, quadratic, exponential, or square root functions.

KNOW

• Find areas of parallelograms, triangles, rhombi, trapezoids, regular polygons, and circles

DO

• Find perimeters and area of parallelograms.

• Determine whether points on a coordinate plane define a parallelogram.

• Find areas of triangles. • Find areas of trapezoids and rhombi. • Find areas of regular polygons.

• Find areas of circles.




GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad (Ch 8.1, 8.2, 8.4 and 8.5)





HISTORICAL/MODERN LINK: Art Connection p. 415 Technology Connection p. 423 Career Connection p. 424, 428

BENCHMARK: (H) Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others. (D) Connect physical, verbal and symbolic representations of

integers, rational numbers and irrational numbers. STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 9 Time Line: 15 days Indicator: #10.12 Make,test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including (a) prove the Pythagorean Theorem. #1. Connect physical, verbal and symbolic representations of irrational numbers; e.g., construct 2 as hypotenuse or on a number line.

KNOW

• Learn to find the geometric mean • Learn the Pythagorean theorem and its

converse.

• Learn that the altitude and the legs are geometric means in a right triangle.

DO

• Find the geometric mean between two numbers

• Find the measure of the altitude drawn to the hypotenuse in a right triangle

• Find the measure of the leg in a right triangle

• Given any two sides of a right triangle

the student will be able to find the length of the third side using Pythagorean theorem.

• Given all three sides of a triangle the

students will be able to identify what type of triangle (right, acute, obtuse)

• Given three order pairs the student will

determine if the segments joining the points form a right triangle based on the distance formula and Pythagorean theorem.

• Learn the properties of special right triangles.

• Learn the trigonometric ratios

• Learn about angles of elevation and depression.

• Given an angle in a right triangle the student will find the lengths of all of the sides of the triangle.

• Given a side in a right triangle the student will find the acute angles of a right triangle.

• Use angles of elevation and depression to solve real world problems.



Quiz 1, 2 and 3 Chapter 9 Test Chapter 9 Constructive Assessment Chapters 7-9 Exam

GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad (Ch 9.1, 9.5 and 9.6)





HISTORICAL/MODERN LINK: History Connection p. 463, 469 Career Connection p. 483 Recreation Connection p. 484 Technology Connection p. 498

BENCHMARK: (E) Estimate and compute various attributes, including length, angle measure, area, surface area an volume, to a specified level of precision

STANDARD: Measurement TOPIC/UNIT: Chapter 10 Time Line: 14 days Indicator: #9.8 (Use Measurement Techniques and Tools) Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively. #9.10 (Use Measurement Techniques and Tools) Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system.

KNOW

• Find volumes of prisms, cylinders,

pyramids, cones, and spheres.

DO

• Students will find volumes of prisms, cylinders, pyramids, cones, and spheres.









HISTORICAL/MODERN LINK: History Connection p. 549 Science Connection p. 504, 520, 537 Career Connection p. 519, 539

BENCHMARK: (B) Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence; STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 11 Time Line: 15 days Indicator: #10.12(b) (Characteristics and Properties) Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including (b) prove theorems involving triangle similarity and congruence. #9.8 (Use Measurement Techniques and Tools) Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively.

KNOW

• Learn to identify similar polygons, and

use ratios and proportions to solve problems.

• Learn to recognize and use proportional parts, corresponding perimeters, altitudes, angle bisectors, and medians or similar triangles to solve problems.

DO

• Determine the ratios and proportions

used to solve problems involving similar polygons.

• Be able to determine whether triangles re similar and be able to solve for missing corresponding parts.

• Be able to prove triangles are similar by AA similarity, SSS similarity, and SAS similarity methods.

• Use construction to trisect a segment.

• Use similar triangles to solve real work

application problems.

• Be able to explain the difference between a median, altitude, angle bisectors, and perpendicular bisector of triangles.






BEST PRACTICES: Cooperative Learning Journal writing p. 618 .



HISTORICAL/MODERN LINK: Art Connection p. 563 Literature Connection p. 613 Career Connection p. 570 History Connection p. 577

BENCHMARK: (H) Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others. (D) Connect physical, verbal and symbolic representations of

integers, rational numbers and irrational numbers. STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 12 Time Line: 13 days Indicator: #10.12 Make,test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including (a) prove the Pythagorean Theorem. #1. Connect physical, verbal and symbolic representations of irrational numbers; e.g., construct 2 as hypotenuse or on a number line.

KNOW

• Learn to find the geometric mean • Learn the Pythagorean theorem and its

converse.

• Learn that the altitude and the legs are geometric means in a right triangle.

DO

• Find the geometric mean between two numbers

• Find the measure of the altitude drawn to the hypotenuse in a right triangle

• Find the measure of the leg in a right triangle

• Given any two sides of a right triangle

the student will be able to find the length of the third side using Pythagorean theorem.

• Given all three sides of a triangle the

students will be able to identify what type of triangle (right, acute, obtuse)

• Given three order pairs the student will

determine if the segments joining the points form a right triangle based on the distance formula and Pythagorean theorem.

• Learn the properties of special right triangles.

• Learn the trigonometric ratios

• Learn about angles of elevation and depression.

• Given an angle in a right triangle the student will find the lengths of all of the sides of the triangle.

• Given a side in a right triangle the student will find the acute angles of a right triangle.

• Use angles of elevation and depression to solve real world problems.





GRAPHIC ORGANIZER & OR TECHNOLOGY: Geometer’s Sketchpad (Ch 12.1, 12.3 and 12.4)





HISTORICAL/MODERN LINK: Science Connection p. 620, 628 Technology Connection p. 630, 648 History Connection p. 638, 639

BENCHMARK: (H) Establish the validity of conjectures about geometric objects; their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others STANDARD: Geometry and Spatial Sense TOPIC/UNIT: Chapter 13 Time Line: 14 days Indicator: #9.1 Identify and justify whether properties (properties of algebra). #10.12(b) (Characteristics and Properties) Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including (b) prove theorems involving triangle similarity and congruence. #9.8 (Use Measurement Techniques and Tools) Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively.

KNOW

• Learn to state conjectures as

conditional statements. • Learn to support statements with

definitions, properties of algebra and equality, and postulates.

• Learn how to write indirect proofs in paragraph form.

• Learn to plan and write coordinate proofs.

DO

• Develop deductive reasoning and

cooperative behavior. • Apply new vocabulary to algebraic and

geometric proofs. • Be able to prove triangles are similar by

AA similarity, SSS similarity, and SAS similarity methods.

• Prove the Angle Bisector Conjecture using triangle congruence.

• Write proofs of parallelogram conjectures.

• Prove circle conjectures. • Use the coordinate proof properties..




GRAPHIC ORGANIZER & OR TECHNOLOGY: Tree Diagrams Pg 683

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: Week 25 of Countdown to OGT p. OH32 textbook




HISTORICAL/MODERN LINK: Mathematics Connection p. 673

10th Grade Honors Geometry - Findlay City · PDF file16 6 Circle Properties...

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Transcript of 10th Grade Honors Geometry - Findlay City · PDF file16 6 Circle Properties...