Practice Your Skills with Answers

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Page i

Discovering

Geometry

An Investigative Approach

Practice Your Skills

with Answers

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7:53 PM

Page ii

Teacher¡¯s Materials Project Editor: Elizabeth DeCarli

Project Administrator: Brady Golden

Coordinating Writer: Jennifer North Morris

Contributors: David Rasmussen, Ralph Bothe, Judy Hicks, Michael Serra

Accuracy Checker: Dudley Brooks

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Composition, Technical Art, Prepress: ICC Macmillan Inc.

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Publisher: Steven Rasmussen

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Your Skills with Answers as part of the Teaching Resources package for the book,

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ISBN 978-1-55953-894-7

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Page iii

Contents

Introduction

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vi

Chapter 1

Lesson 1.1:

Lesson 1.2:

Lesson 1.3:

Lesson 1.4:

Lesson 1.5:

Lesson 1.6:

Lesson 1.7:

Lesson 1.8:

Lesson 1.9:

Building Blocks of Geometry . . . . . . .

Poolroom Math . . . . . . . . . . . . . . . . . . . .

What¡¯s a Widget? . . . . . . . . . . . . . . . . . .

Polygons . . . . . . . . . . . . . . . . . . . . . . . . . .

Triangles . . . . . . . . . . . . . . . . . . . . . . . . . .

Special Quadrilaterals . . . . . . . . . . . . . .

Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Space Geometry . . . . . . . . . . . . . . . . . . .

A Picture Is Worth a Thousand Words

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1

2

3

4

5

6

7

8

9

Chapter 2

Lesson 2.1:

Lesson 2.2:

Lesson 2.3:

Lesson 2.4:

Lesson 2.5:

Lesson 2.6:

Inductive Reasoning . . . . . . . . . .

Finding the nth Term . . . . . . . . .

Mathematical Modeling . . . . . . .

Deductive Reasoning . . . . . . . . .

Angle Relationships . . . . . . . . . . .

Special Angles on Parallel Lines

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10

11

12

13

14

15

Chapter 3

Lesson 3.1:

Lesson 3.2:

Lesson 3.3:

Lesson 3.4:

Lesson 3.5:

Lesson 3.6:

Lesson 3.7:

Lesson 3.8:

Duplicating Segments and Angles . . .

Constructing Perpendicular Bisectors .

Constructing Perpendiculars to a Line

Constructing Angle Bisectors . . . . . . . .

Constructing Parallel Lines . . . . . . . . . .

Construction Problems . . . . . . . . . . . . . .

Constructing Points of Concurrency . .

The Centroid . . . . . . . . . . . . . . . . . . . . . . .

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16

17

18

19

20

21

22

23

Chapter 4

Lesson 4.1:

Lesson 4.2:

Lesson 4.3:

Lesson 4.4:

Lesson 4.5:

Lesson 4.6:

Lesson 4.7:

Lesson 4.8:

Triangle Sum Conjecture . . . . . . . . . . . . . . . . . .

Properties of Isosceles Triangles . . . . . . . . . . .

Triangle Inequalities . . . . . . . . . . . . . . . . . . . . . .

Are There Congruence Shortcuts? . . . . . . . . . .

Are There Other Congruence Shortcuts? . . . .

Corresponding Parts of Congruent Triangles

Flowchart Thinking . . . . . . . . . . . . . . . . . . . . . . .

Proving Special Triangle Conjectures . . . . . . .

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24

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26

27

28

29

30

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Chapter 5

Lesson 5.1:

Lesson 5.2:

Lesson 5.3:

Lesson 5.4:

Lesson 5.5:

Lesson 5.6:

Lesson 5.7:

Polygon Sum Conjecture . . . . . . . . . .

Exterior Angles of a Polygon . . . . . .

Kite and Trapezoid Properties . . . . .

Properties of Midsegments . . . . . . . .

Properties of Parallelograms . . . . . . .

Properties of Special Parallelograms

Proving Quadrilateral Properties . . .

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32

33

34

35

36

37

38

Chapter 6

Lesson 6.1: Tangent Properties . . . . . . . . . . . . . . . . . . . . . . .

Lesson 6.2: Chord Properties . . . . . . . . . . . . . . . . . . . . . . . . .

Lesson 6.3: Arcs and Angles . . . . . . . . . . . . . . . . . . . . . . . . . .

Lesson 6.4: Proving Circle Conjectures . . . . . . . . . . . . . . . . .

Lesson 6.5: The Circumference/Diameter Ratio . . . . . . . . .

Lesson 6.6: Around the World . . . . . . . . . . . . . . . . . . . . . . . .

Lesson 6.7: Arc Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Exploration: Intersecting Secants, Tangents, and Chords

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39

40

41

42

43

44

45

46

Chapter 7

Lesson 7.1: Transformations and Symmetry . . . .

Lesson 7.2: Properties of Isometries . . . . . . . . . . .

Lesson 7.3: Compositions of Transformations . .

Lesson 7.4: Tessellations with Regular Polygons

Lessons 7.5¨C7.8: Tessellations . . . . . . . . . . . . . . . . .

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48

49

50

51

Chapter 8

Lesson 8.1:

Lesson 8.2:

Lesson 8.3:

Lesson 8.4:

Lesson 8.5:

Lesson 8.6:

Lesson 8.7:

Areas of Rectangles and Parallelograms

Areas of Triangles, Trapezoids, and Kites

Area Problems . . . . . . . . . . . . . . . . . . . . . . . .

Areas of Regular Polygons . . . . . . . . . . . . .

Areas of Circles . . . . . . . . . . . . . . . . . . . . . . .

Any Way You Slice It . . . . . . . . . . . . . . . . . .

Surface Area . . . . . . . . . . . . . . . . . . . . . . . . .

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52

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58

Chapter 9

Lesson 9.1:

Lesson 9.2:

Lesson 9.3:

Lesson 9.4:

Lesson 9.5:

Lesson 9.6:

iv

The Theorem of Pythagoras . . . . . . . . . . . . . .

The Converse of the Pythagorean Theorem

Two Special Right Triangles . . . . . . . . . . . . . . .

Story Problems . . . . . . . . . . . . . . . . . . . . . . . . . .

Distance in Coordinate Geometry . . . . . . . . .

Circles and the Pythagorean Theorem . . . . .

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Chapter 10

Lesson 10.1:

Lesson 10.2:

Lesson 10.3:

Lesson 10.4:

Lesson 10.5:

Lesson 10.6:

Lesson 10.7:

The Geometry of Solids . . . . . . . .

Volume of Prisms and Cylinders

Volume of Pyramids and Cones .

Volume Problems . . . . . . . . . . . . . .

Displacement and Density . . . . .

Volume of a Sphere . . . . . . . . . . . .

Surface Area of a Sphere . . . . . . .

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66

67

68

69

70

71

Chapter 11

Lesson 11.1:

Lesson 11.2:

Lesson 11.3:

Lesson 11.4:

Lesson 11.5:

Lesson 11.6:

Lesson 11.7:

Similar Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Similar Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Indirect Measurement with Similar Triangles . .

Corresponding Parts of Similar Triangles . . . . .

Proportions with Area . . . . . . . . . . . . . . . . . . . . . .

Proportions with Volume . . . . . . . . . . . . . . . . . . . .

Proportional Segments Between Parallel Lines

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78

Chapter 12

Lesson 12.1:

Lesson 12.2:

Lesson 12.3:

Lesson 12.4:

Lesson 12.5:

Trigonometric Ratios . . . . . . . . . . . . . . . .

Problem Solving with Right Triangles

The Law of Sines . . . . . . . . . . . . . . . . . . .

The Law of Cosines . . . . . . . . . . . . . . . . .

Problem Solving with Trigonometry . .

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Chapter 13

Lesson 13.1:

Lesson 13.2:

Lesson 13.3:

Lesson 13.4:

Lesson 13.5:

Lesson 13.6:

Lesson 13.7:

Answers

The Premises of Geometry

Planning a Geometry Proof

Triangle Proofs . . . . . . . . . .

Quadrilateral Proofs . . . . . .

Indirect Proof . . . . . . . . . . . .

Circle Proofs . . . . . . . . . . . . .

Similarity Proofs . . . . . . . . . .

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90

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