Discovering Geometry - Flourish

1 DG3SM586_ 8/2/06 6:45 PM Page i Discovering Geometry An Investigative Approach Solutions Manual DG3SM586_ 1/3/07 4:34 PM Page ii Teacher's Materials Project Editor: Joan Lewis Editor: Heather Dever Project Manager: Erin Gray Writers: Abby Tanenbaum, Stacey Miceli Editorial Assistants: Lori Dixon, Karen Rodriguez'G. Accuracy Checker: Dudley Brooks Production Editors: Jacqueline Gamble, Angela Chen Copyeditor: Margaret Moore Editorial Production Manager: Deborah Cogan Production Director: Diana Jean Parks Production Coordinator: Ann Rothenbuhler Text Designers: Jenny Somerville, Garry Harman Art Editor: Jason Luz Composition, Technical Art: Interactive Composition Corporation Art and Design Coordinator: Caroline Ayres Cover Designer: Jill Kongabel Printer, Prepress: Data Reproductions Executive Editor: Casey FitzSimons Publisher.

2 Steven Rasmussen 2003 by Key Curriculum Press. 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 who purchases Discovering Geometry : An Investigative Approach, Solutions Manual the right to reproduce material for use in his or her own classroom. Unauthorized copying of Discovering Geometry : An Investigative Approach, Solutions Manual constitutes copyright infringement and is a violation of federal law.

3 Key Curriculum Press is a registered trademark of Key Curriculum Press. All registered trademarks and trademarks in this book are the property of their respective holders. Key Curriculum Press 1150 65th Street Emeryville, CA 94608. 510-595-7000. Printed in the United States of America 10 9 8 7 6 09 08 07 ISBN 978-1-55953-586-1. DG3SM586_ 8/2/06 6:45 PM Page iii Introduction Contents Introduction .. vii Chapter 0. Lesson : Geometry in Nature and in Art .. 1. Lesson : Line Designs .. 1. Lesson : Circle Designs .. 2. Lesson : Op Art .. 4. Lesson : Knot Designs.

4 4. Lesson : Islamic Tile Designs .. 5. Chapter 0 Review .. 6. Chapter 1. Lesson : Building Blocks of Geometry .. 7. Using Your Algebra Skills 1: Midpoint .. 8. Lesson : Poolroom Math .. 9. Lesson : What's a Widget? .. 11. Lesson : Polygons .. 13. Lesson : Triangles and Special Quadrilaterals .. 15. Lesson : Circles .. 17. Lesson : A Picture Is Worth a Thousand Words .. 19. Lesson : Space Geometry .. 21. Chapter 1 Review .. 24. Chapter 2. Lesson : Inductive Reasoning .. 25. Lesson : Deductive Reasoning .. 27. Lesson : Finding the nth Term .. 29. Lesson : Mathematical Modeling.

5 30. Lesson : Angle Relationships .. 32. Lesson : Special Angles on Parallel Lines .. 34. Using Your Algebra Skills 2: Slope .. 35. Chapter 2 Review .. 36. Chapter 3. Lesson : Duplicating Segments and Angles .. 37. Lesson : Constructing Perpendicular Bisectors .. 39. Lesson : Constructing Perpendiculars to a Line .. 41. Lesson : Constructing Angle Bisectors .. 43. Lesson : Constructing Parallel Lines .. 45. Using Your Algebra Skills 3: Slopes of Parallel and Perpendicular Lines .. 46. iii DG3SM586_ 8/2/06 6:45 PM Page iv Lesson : Construction Problems.

6 47. Exploration: Perspective Drawing .. 50. Lesson : Constructing Points of Concurrency .. 50. Lesson : The Centroid .. 52. Exploration: The Euler Line .. 54. Chapter 3 Review .. 54. Chapter 4. Lesson : Triangle Sum Conjecture .. 56. Lesson : Properties of Special Triangles .. 58. Using Your Algebra Skills 4: Writing Linear Equations .. 61. Lesson : Triangle Inequalities .. 63. Lesson : Are There Congruence Shortcuts? .. 64. Lesson : Are There Other Congruence Shortcuts? .. 66. Lesson : Corresponding Parts of Congruent Triangles .. 68. Lesson : Flowchart Thinking.

7 69. Lesson : Proving Isosceles Triangle Conjectures .. 71. Exploration: Napoleon's Theorem .. 72. Chapter 4 Review .. 72. Take Another Look .. 74. Chapter 5. Lesson : Polygon Sum Conjecture .. 75. Lesson : Exterior Angles of a Polygon .. 78. Lesson : Kite and Trapezoid Properties .. 79. Lesson : Properties of Midsegments .. 81. Lesson : Properties of Parallelograms .. 84. Using Your Algebra Skills 5: Solving Systems of Linear Equations .. 86. Lesson : Properties of Special Parallelograms .. 88. Lesson : Proving Quadrilateral Properties .. 91. Chapter 5 Review.

8 93. Take Another Look .. 96. Chapter 6. Lesson : Chord Properties .. 97. Lesson : Tangent Properties .. 99. Lesson : Arcs and Angles .. 102. Lesson : Proving Circle Conjectures .. 105. Using Your Algebra Skills 6: Finding the Circumcenter .. 107. Lesson : The Circumference/Diameter Ratio .. 110. Lesson : Around the World .. 112. Lesson : Arc Length .. 113. Exploration: Cycloids .. 115. Chapter 6 Review .. 116. Take Another Look .. 120. iv DG3SM586_ 8/2/06 6:45 PM Page v Chapter 7. Lesson : Transformations and Symmetry .. 120. Lesson : Properties of Isometries.

9 122. Lesson : Compositions of Transformations .. 125. Lesson : Tessellations with Regular Polygons .. 127. Lesson : Tessellations with Nonregular Polygons .. 129. Lesson : Tessellations Using Only Translations .. 130. Lesson : Tessellations That Use Rotations .. 130. Lesson : Tessellations That Use Glide Reflections .. 131. Using Your Algebra Skills 7: Finding the Orthocenter and Centroid .. 132. Chapter 7 Review .. 134. Chapter 8. Lesson : Areas of Rectangles and Parallelograms .. 136. Lesson : Areas of Triangles, Trapezoids, and Kites .. 138. Lesson : Area Problems.

10 142. Lesson : Areas of Regular Polygons .. 144. Lesson : Areas of Circles .. 146. Lesson : Any Way You Slice It .. 147. Exploration: Geometric Probability II .. 149. Lesson : Surface Area .. 149. Exploration: Alternative Area Formulas .. 151. Chapter 8 Review .. 152. Take Another Look .. 155. Chapter 9. Lesson : The Theorem of Pythagoras .. 156. Lesson : The Converse of the Pythagorean Theorem .. 159. Using Your Algebra Skills 8: Radical Expressions .. 161. Lesson : Two Special Right Triangles .. 162. Lesson : Story Problems .. 165. Lesson : Distance in Coordinate Geometry .