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Discovering Geometry an Investigative Approach

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Discovering Geometry an Investigative Approach Discovering Geometry An Investigative Approach Condensed Lessons: A Tool for Parents and Tutors Teacher’s Materials Project Editor: Elizabeth DeCarli Project Administrator: Brady Golden Writers: David Rasmussen, Stacey Miceli Accuracy Checker: Dudley Brooks Production Editor: Holly Rudelitsch Copyeditor: Jill Pellarin Editorial Production Manager: Christine Osborne Production Supervisor: Ann Rothenbuhler Production Coordinator: Jennifer Young Text Designers: Jenny Somerville, Garry Harman Composition, Technical Art, Prepress: ICC Macmillan Inc. Cover Designers: Jill Kongabel, Marilyn Perry, Jensen Barnes Printer: Data Reproductions Textbook Product Manager: James Ryan Executive Editor: Casey FitzSimons Publisher: Steven Rasmussen ©2008 by Kendall Hunt Publishing. All rights reserved. Cover Photo Credits: Background image: Doug Wilson/Westlight/Corbis. Construction site image: Sonda Dawes/The Image Works. All other images: Ken Karp Photography. Limited Reproduction Permission The publisher grants the teacher whose school has adopted Discovering Geometry, and who has received Discovering Geometry: An Investigative Approach, Condensed Lessons: A Tool for Parents and Tutors as part of the Teaching Resources package for the book, the right to reproduce material for use in his or her own classroom. Unauthorized copying of Discovering Geometry: An Investigative Approach, Condensed Lessons: A Tool for Parents and Tutors constitutes copyright infringement and is a violation of federal law. All registered trademarks and trademarks in this book are the property of their respective holders. Kendall Hunt Publishing 4050 Westmark Drive PO Box 1840 Dubuque, IA 52004-1840 www.kendallhunt.com Printed in the United States of America 10 9 8 7 6 5 4 3 2 13 12 11 10 09 08 ISBN 978-1-55953-895-4 Contents Introduction . vi Chapter 1 Lesson 1.1: Building Blocks of Geometry . 1 Lesson 1.2: Poolroom Math . 3 Lesson 1.3: What’s a Widget? . 5 Lesson 1.4: Polygons . 7 Lesson 1.5: Triangles . 9 Lesson 1.6: Special Quadrilaterals . 11 Lesson 1.7: Circles . 13 Lesson 1.8: Space Geometry . 15 Lesson 1.9: A Picture Is Worth a Thousand Words . 17 Chapter 2 Lesson 2.1: Inductive Reasoning . 19 Lesson 2.2: Finding the nth Term . 21 Lesson 2.3: Mathematical Modeling . 23 Lesson 2.4: Deductive Reasoning . 25 Lesson 2.5: Angle Relationships . 27 Lesson 2.6: Special Angles on Parallel Lines . 29 Chapter 3 Lesson 3.1: Duplicating Segments and Angles . 31 Lesson 3.2: Constructing Perpendicular Bisectors . 33 Lesson 3.3: Constructing Perpendiculars to a Line . 35 Lesson 3.4: Constructing Angle Bisectors . 37 Lesson 3.5: Constructing Parallel Lines . 39 Lesson 3.6: Construction Problems . 41 Lesson 3.7: Constructing Points of Concurrency . 43 Lesson 3.8: The Centroid . 47 Chapter 4 Lesson 4.1: Triangle Sum Conjecture . 49 Lesson 4.2: Properties of Isosceles Triangles . 51 Lesson 4.3: Triangle Inequalities . 53 Lesson 4.4: Are There Congruence Shortcuts? . 55 Lesson 4.5: Are There Other Congruence Shortcuts? . 57 Lesson 4.6: Corresponding Parts of Congruent Triangles . 59 Lesson 4.7: Flowchart Thinking . 61 Lesson 4.8: Proving Special Triangle Conjectures . 63 iii Chapter 5 Lesson 5.1: Polygon Sum Conjecture . 65 Lesson 5.2: Exterior Angles of a Polygon . 67 Lesson 5.3: Kite and Trapezoid Properties . 69 Lesson 5.4: Properties of Midsegments . 71 Lesson 5.5: Properties of Parallelograms . 73 Lesson 5.6: Properties of Special Parallelograms . 75 Lesson 5.7: Proving Quadrilateral Properties . 77 Chapter 6 Lesson 6.1: Tangent Properties . 79 Lesson 6.2: Chord Properties . 81 Lesson 6.3: Arcs and Angles . 83 Lesson 6.4: Proving Circle Conjectures . 85 Lesson 6.5: The Circumference/Diameter Ratio . 87 Lesson 6.6: Around the World . 89 Lesson 6.7: Arc Length . 91 Chapter 7 Lesson 7.1: Transformations and Symmetry . 93 Lesson 7.2: Properties of Isometries . 95 Lesson 7.3: Compositions of Transformations . 97 Lesson 7.4: Tessellations with Regular Polygons . 99 Lesson 7.5: Tessellations with Nonregular Polygons . 101 Chapter 8 Lesson 8.1: Areas of Rectangles and Parallelograms . 103 Lesson 8.2: Areas of Triangles, Trapezoids, and Kites . 105 Lesson 8.3: Area Problems . 107 Lesson 8.4: Areas of Regular Polygons . 109 Lesson 8.5: Areas of Circles . 111 Lesson 8.6: Any Way You Slice It . 113 Lesson 8.7: Surface Area . 115 Chapter 9 Lesson 9.1: The Theorem of Pythagoras . 119 Lesson 9.2: The Converse of the Pythagorean Theorem . 121 Lesson 9.3: Two Special Right Triangles . 123 Lesson 9.4: Story Problems . 125 Lesson 9.5: Distance in.
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