# The Complete Idiot's Guide to Geometry

Penguin, 2004 - Mathematics - 376 pages
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Geometry is hard. This book makes it easier. You do the math. This is the fourth title in the series designed to help high school and college students through a course they'd rather not be taking. A non-intimidating, easy- to-understand companion to their textbook, this book takes students through the standard curriculum of topics, including proofs, polygons, coordinates, topology, and much more.

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### Contents

 The Foundation 1 What Is Geometry Anyway? 3 Whats the Point? 4 Getting Into Shape 5 Learning How to Write Proofs 6 And the Winner Is Euclid 7 A Goliath Mathematician 9 Can I Really Learn This? 10
 Opening Doors with Similar Triangles 167 The Pythagorean Theorem 168 Parallel Segments and Segment Proportions 170 Three Famous Triangles 173 306090 Triangle 174 454590 Triangle 176 Putting Quadrilaterals in the Forefront 179 Properties of All Quadrilaterals 180

 Lets Do Algebra 13 Long Lost Relations 14 Properties of Equality 15 Reflexive Symmetric and Transitive Properties 16 Algebraic Properties of Equality 17 The Square Root Property of Equality 19 Properties of Inequality 20 Is It an Equivalence Relation? 21 An Additional Additive Property 22 Building Blocks 25 Coming to Terms 26 Lines 28 Line Segments 29 Segment Length 30 A New Relation 31 Segment Addition 32 Rays 33 Planes 34 Theres Always an Angle 37 Whats in a Name? 38 Are You My Type? The Basic Angle Classifications 40 Angle Addition 41 How Do Angles Relate? Classifying Pairs of Angles 42 Congruent Angles 43 Complementary and Supplementary Angles 44 A First Look at Proving Angle Congruence 46 Lines and the Angles They Form 49 Linear Interactions 50 Perpendicular Lines 52 Euclids 5th 55 Transversals and the New Angle Pairs 57 A Polygon Is a ManySided Thing 59 Coming to Terms with the Terminology 60 Naming Conventions and Classifications 63 The Interior Angles 64 Regular Polygons 67 Introducing Proofs 71 Logic Rules for Arguing 73 Inductive Reasoning 74 Elementary My Dear Watson 75 Logical Constructions and Truth Tables 76 Conjunction 77 Disjunction 78 Implication or Conditional 79 Logical Equivalence and Tautology 81 Taking the Burden out of Proofs 85 The Law of Detachment 86 The Importance of Being Direct 87 The Advantage of Being Indirect 89 Use It or Lose It 90 What Should You Bring to a Formal Proof? 92 Proving Segment and Angle Relationships 97 Exploring Midpoints 98 How Many Midpoints Are There? 99 Proving Angles Are Congruent 101 Using and Proving Angle Complements 102 Using and Proving Angle Supplements 105 Proving Relationships Between Lines 109 Proofs Involving Perpendicular Lines 110 Lets Get Parallel 112 Proofs About Alternate Angles 113 Parallel Lines and Supplementary Angles 115 Using Parallelism to Prove Perpendicularity 116 Proving Lines Are Parallel 117 Piecing Together Triangles and Quadrilaterals 123 Twos Company Threes a Triangle 125 A Formal Introduction 126 Sums of Interior Angles Are Cooking at 180 128 Exterior Angle Relationships 130 Size Matters So Lets Measure 132 The Pythagorean Theorem 134 The Triangle Inequality 135 Congruent Triangles 139 CPOCTAC 140 The SSS Postulate 141 The SAS Postulate 142 The ASA Postulate 144 The AAS Theorem 145 The HL Theorem for Right Triangles 146 Proving Segments and Angles Are Congruent 149 Proving Lines Are Parallel 150 Similar Triangles 155 Ratio Proportion and Geometric Means 156 Properties of Similar Triangles 159 The Big Three 161 The SAS and SSS Similarity Theorems 164
 Lets All Fly a Kite 182 Properties of Parallelograms 184 The Most Popular Parallelograms 186 Rhombuses 187 Squares 189 Area of Parallelograms 190 The Pythagorean Theorem again 191 Proofs About Quadrilaterals 195 When Is a Quadrilateral a Parallelogram? 196 Two Pairs of Congruent Sides 197 Two Pairs of Congruent Angles 199 Bisecting Diagonals 200 When Is a Parallelogram a Rectangle? 201 When Is a Parallelogram a Rhombus? 202 When Is a Parallelogram a Square? 204 Going Around in Circles 207 Anatomy of a Circle 209 Basic Terms 210 Arcs 211 Pi Anyone? 215 Tangents 217 From One Theorem Comes Many 218 Segments and Angles 225 Angles and Chords 226 Arcs and Chords 227 Radii and Chords 229 Putting the Pieces Together 233 Circular Arguments 237 Angles and Arcs 238 Similarity 241 Parallel Chords and Arcs 245 Putting Your Problems Behind You 247 The Unit Circle and Trigonometry 251 The Tangent Ratio 252 The Sine Ratio 255 The Cosine Ratio 257 And the Rest 259 How Does This Relate to the Unit Circle? 261 Where Can We Go from Here? 267 The Next Dimension Surfaces and Solids 269 Prisms 270 Pyramids 273 Cylinders and Cones 274 Polyhedra 276 Spheres 277 Platonic Solids 278 Under Construction 281 Tools of the Trade 282 Compass 283 Bisection 284 Bisecting Angles 285 Constructing Lines 287 Parallel Lines 289 Constructing Quadrilaterals 290 Parallelograms 291 Squares 292 When Geometry and Algebra Intersect 293 The Cartesian Coordinate System 294 Finding Horizontal and Vertical Distances 295 The Pythagorean Theorem Goes the Distance 296 The Midpoint Formula 297 Finding Equations of Lines 298 The PointSlope Formula 300 The Secret Lives of Parallel and Perpendicular Lines 301 A Picture Is Worth a Thousand Words 302 Whose Geometry Is It Anyway? 305 NonEuclidean Geometry 306 Saddle Up 307 Spherical Geometry 309 TaxiCab Geometry 310 Max Geometry 312 How Many Shapes Can a Circle Have? 313 Transformations 317 Isometrics 318 Translations 319 Reflections 320 Rotations 322 Glide Reflections 324 Dilations 325 Symmetry 326 Answer Key 331 Postulates and Theorems 351 Formulas 357 Glossary 359 Index 367 Copyright