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CK-12 Geometry - Second Edition, Answer Key CK-12 Foundation Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org AUTHOR CK-12 Foundation To access a customizable version of this book, as well as other interactive content, visit www.ck12.org CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web- based collaborative model termed the FlexBook®textbook, CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform®. Copyright © 2015 CK-12 Foundation, www.ck12.org The names “CK-12” and “CK12” and associated logos and the terms “FlexBook®” and “FlexBook Platform®” (collectively “CK-12 Marks”) are trademarks and service marks of CK-12 Foundation and are protected by federal, state, and international laws. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link http://www.ck12.org/saythanks (placed in a visible location) in addition to the following terms. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution-Non-Commercial 3.0 Unported (CC BY-NC 3.0) License (http://creativecommons.org/ licenses/by-nc/3.0/), as amended and updated by Creative Com- mons from time to time (the “CC License”), which is incorporated herein by this reference. Complete terms can be found at http://www.ck12.org/about/ terms-of-use. Printed: February 25, 2015 iii Contents www.ck12.org Contents 1 Basics of Geometry, Answer Key1 1.1 Geometry - Second Edition, Points, Lines, and Planes, Review Answers ............. 2 1.2 Geometry - Second Edition, Segments and Distance, Review Answers.............. 5 1.3 Geometry - Second Edition, Angles and Measurement, Review Answers............. 7 1.4 Geometry - Second Edition, Midpoints and Bisectors, Review Answers.............. 10 1.5 Geometry - Second Edition, Angle Pairs, Review Answers .................... 13 1.6 Geometry - Second Edition, Classifying Polygons, Review Answers ............... 14 1.7 Geometry - Second Edition, Chapter Review Answers....................... 17 2 Reasoning and Proof, Answer Key 18 2.1 Geometry - Second Edition, Inductive Reasoning, Review Answers................ 19 2.2 Geometry - Second Edition, Conditional Statements, Review Answers.............. 21 2.3 Geometry - Second Edition, Deductive Reasoning, Review Answers ............... 23 2.4 Geometry - Second Edition, Algebraic and Congruence Properties, Review Answers . 26 2.5 Geometry - Second Edition, Proofs about Angle Pairs and Segments, Review Answers . 29 2.6 Chapter Review Answers...................................... 33 3 Parallel and Perpendicular Lines, Answer Key 34 3.1 Geometry - Second Edition, Lines and Angles, Review Answers ................. 35 3.2 Geometry - Second Edition, Properties of Parallel Lines, Review Answers............ 37 3.3 Geometry - Second Edition, Proving Lines Parallel, Review Answers............... 40 3.4 Geometry - Second Edition, Properties of Perpendicular Lines, Review Answers......... 42 3.5 Geometry - Second Edition, Parallel and Perpendicular Lines in the Coordinate Plane, Review Answers............................................... 43 3.6 Geometry - Second Edition, The Distance Formula, Review Answers............... 47 3.7 Chapter Review Answers...................................... 49 4 Triangles and Congruence, Answer key 50 4.1 Geometry - Second Edition, Triangle Sums, Review Answers................... 51 4.2 Geometry - Second Edition, Congruent Figures, Review Answers................. 53 4.3 Geometry - Second Edition, Triangle Congruence using SSS and SAS, Review Answers . 55 4.4 Geometry - Second Edition, Triangle Congruence using ASA, AAS, and HL, Review Answers . 58 4.5 Geometry - Second Edition, Isosceles and Equilateral Triangles, Review Answers . 60 4.6 Chapter 4 Review Answers..................................... 63 5 Relationships with Triangles, Answer Key 64 5.1 Geometry - Second Edition, Midsegments of a Triangle, Review Answers ............ 65 5.2 Geometry - Second Edition, Perpendicular Bisectors in Triangles, Review Answers . 67 5.3 Geometry - Second Edition, Angle Bisectors in Triangles, Review Answers ........... 71 5.4 Geometry - Second Edition, Medians and Altitudes in Triangles, Review Answers . 73 5.5 Geometry - Second Edition, Inequalities in Triangles, Review Answers.............. 75 5.6 Geometry - Second Edition, Extension: Indirect Proof, Review Answers............. 76 iv www.ck12.org Contents 5.7 Chapter Review Answers...................................... 77 6 Polygons and Quadrilaterals, Answer Key 78 6.1 Geometry - Second Edition, Angles in Polygons, Review Answers ................ 79 6.2 Geometry - Second Edition, Properties of Parallelograms, Review Answers ........... 81 6.3 Geometry - Second Edition, Proving Quadrilaterals are Parallelograms, Review Answers . 83 6.4 Geometry - Second Edition, Rectangles, Rhombuses and Squares, Review Answers . 86 6.5 Geometry - Second Edition, Trapezoids and Kites, Review Answers ............... 89 6.6 Chapter Review Answers...................................... 91 7 Similarity, Answer Key 92 7.1 Geometry - Second Edition, Ratios and Proportions, Review Answers .............. 93 7.2 Geometry - Second Edition, Similar Polygons, Review Answers ................. 94 7.3 Geometry - Second Edition, Similarity by AA, Review Answers ................. 95 7.4 Geometry - Second Edition, Similarity by SSS and SAS, Review Answers............ 96 7.5 Geometry - Second Edition, Proportionality Relationships, Review Answers........... 97 7.6 Geometry - Second Edition, Similarity Transformations, Review Answers ............ 99 7.7 Geometry - Second Edition, Extension: Self-Similarity, Review Answers . 101 7.8 Chapter Review Answers......................................103 8 Right Triangle Trigonometry, Answer Key 104 8.1 Geometry - Second Edition, The Pythagorean Theorem, Review Answers . 105 8.2 Geometry - Second Edition, Converse of the Pythagorean Theorem, Review Answers . 106 8.3 Geometry - Second Edition, Using Similar Right Triangles, Review Answers . 109 8.4 Geometry - Second Edition, Special Right Triangles, Review Answers . 111 8.5 Geometry - Second Edition, Tangent, Sine and Cosine, Review Answers . 112 8.6 Geometry - Second Edition, Inverse Trigonometric Ratios, Review Answers . 113 8.7 Geometry - Second Edition, Extension: Laws of Sines and Cosines, Review Answers . 114 8.8 Chapter Review Answers......................................115 9 Circles, Answer Key 116 9.1 Geometry - Second Edition, Parts of Circles and Tangent Lines, Review Answers . 117 9.2 Geometry - Second Edition, Properties of Arcs, Review Answers . 119 9.3 Geometry - Second Edition, Properties of Chords, Review Answers . 120 9.4 Geometry - Second Edition, Inscribed Angles, Review Answers..................122 9.5 Geometry - Second Edition, Angles of Chords, Secants, and Tangents, Review Answers . 124 9.6 Geometry - Second Edition, Segments of Chords, Secants, and Tangents, Review Answers . 127 9.7 Geometry - Second Edition, Extension: Writing and Graphing the Equations of Circles, Review Answers...............................................128 9.8 Chapter Review Answers......................................129 10 Perimeter and Area, Answer Key 130 10.1 Geometry - Second Edition, Triangles and Parallelograms, Review Answers . 131 10.2 Geometry - Second Edition, Trapezoids, Rhombi, and Kites, Review Answers . 132 10.3 Geometry - Second Edition, Areas of Similar Polygons, Review Answers . 134 10.4 Geometry - Second Edition, Circumference and Arc Length, Review Answers . 135 10.5 Geometry - Second Edition, Areas of Circles and Sectors, Review Answers . 136 10.6 Geometry - Second Edition, Area and Perimeter of Regular Polygons, Review Answers . 137 10.7 Chapter Review Answers......................................139 11 Surface Area and Volume, Answer Key 140 11.1 Geometry - Second Edition, Exploring Solids, Review Answers..................141 v Contents www.ck12.org 11.2 Geometry - Second Edition, Surface Area of Prisms and Cylinders, Review Answers . 143 11.3 Geometry - Second Edition, Surface Area of Pyramids and Cones, Review Answers . 144 11.4 Geometry - Second Edition, Volume of Prisms and Cylinders, Review Answers . 146 11.5 Geometry - Second Edition, Volume of Pyramids and Cones, Review Answers . 147 11.6 Geometry - Second Edition, Surface Area and Volume of Spheres, Review Answers . 148 11.7 Geometry - Second Edition, Exploring Similar Solids, Review Answers . 150 11.8 Chapter Review Answers......................................151 12 Rigid Transformations, Answer Key 152 12.1 Geometry - Second Edition, Exploring Symmetry, Review Answers . 153 12.2 Geometry - Second Edition, Translations and Vectors , Review Answers . 155 12.3 Geometry - Second Edition, Reflections, Review Answers.....................156 12.4 Geometry - Second Edition, Rotations, Review Answers......................158 12.5 Geometry - Second Edition, Composition of Transformations, Review Answers . 162 12.6 Geometry - Second Edition, Extension: Tessellations, Review Answers . 163 12.7 Chapter Review Answers......................................164 vi www.ck12.org Chapter 1. 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