Table of Contents

Introduction 1

Part 1: Getting Started with Geometry Basics 5

Chapter 1: Introducing Geometry 7

Chapter 2: Building Your Geometric Foundation 17

Chapter 3: Sizing Up Segments and Analyzing Angles 31

Part 2: Introducing Proofs 43

Chapter 4: Prelude to Proofs 45

Chapter 5: Your Starter Kit of Easy Theorems and Short Proofs 55

Chapter 6: The Ultimate Guide to Tackling a Longer Proof 75

Part 3: Triangles: Polygons of the Three-Sided Variety 87

Chapter 7: Grasping Triangle Fundamentals 89

Chapter 8: Regarding Right Triangles 107

Chapter 9: Completing Congruent Triangle Proofs 125

Part 4: Polygons of the Four-or-More-Sided Variety 153

Chapter 10: The Seven Wonders of the Quadrilateral World 155

Chapter 11: Proving That You Have a Particular Quadrilateral 177

Chapter 12: Polygon Formulas: Area, Angles, and Diagonals 193

Chapter 13: Similarity: Same Shape, Different Size 211

Part 5: Working with Not-So-Vicious Circles 235

Chapter 14: Coming Around to Circle Basics 237

Chapter 15: Circle Formulas and Theorems 255

Part 6: Going Deep with 3-D Geometry 277

Chapter 16: 3-D Space: Proofs in a Higher Plane of Existence 279

Chapter 17: Getting a Grip on Solid Geometry 287

Part 7: Placement, Points, and Pictures: Alternative Geometry Topics 303

Chapter 18: Coordinate Geometry 305

Chapter 19: Changing the Scene with Geometric Transformations 323

Chapter 20: Locating Loci and Constructing Constructions 343

Part 8: The Part of Tens 361

Chapter 21: Ten Things to Use as Reasons in Geometry Proofs 363

Chapter 22: Ten Cool Geometry Problems 369

Index 377

About the Author

Mark Ryan is the founder and owner of The Math Center in the Chicago area, where he provides tutoring in all math subjects as well as test preparation. Mark is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.