Geometry Workbook For Dummies

Mark Ryan, a graduate of Brown University and the University of Wisconsin Law School, has been teaching math since 1989. He runs the Math Center in Winnetka, Illinois (www.themathcenter.com), where he teaches high school math courses including an introduction to geometry and a workshop for parents based on a program he developed, The 10 Habits of Highly Successful Math Students. In high school, he twice scored a perfect 800 on the math portion of the SAT, and he not only knows mathematics, he has a gift for explaining it in plain English. He practiced law for four years before deciding he should do something he enjoys and use his natural talent for mathematics. Ryan is a member of the Authors Guild and the National Council of Teachers of Mathematics. Geometry Workbook For Dummies is Ryans fourth book. Everyday Math for Everyday Life was published in 2002, Calculus For Dummies (Wiley) in 2003, and Calculus Workbook For Dummies in 2005. His math books have sold over 100,000 copies.

Introduction 1 About This Book 1 Conventions Used in This Book 2 How to Use This Book 2 Foolish Assumptions 2 How This Book is Organized 3 Part I: Getting Started 3 Part II: Triangles 3 Part III: Polygons 3 Part IV: Circles 4 Part V: 3-D Geometry and Coordinate Geometry 4 Part VI: The Part of Tens 4 Icons Used in This Book 4 Where to Go from Here 5 Part I: Getting Started 7 Chapter 1: Introducing Geometry and Geometry Proofs! 9 Making the Right Assumptions: What is Geometry? 9 If-Then Logic: If You Bought This Book, Then You Must Love Geometry! 12 Discovering Geometry Proofs 14 Solutions for Introducting Geometry and Geometry Proofs! 17 Chapter 2: Points, Segments, Lines, Rays, and Angles 19 Basic Definitions 19 Union and Intersection Problems 20 Division in the Ranks: Bisection and Trisection 22 Perfect Hilarity for Perpendicularity 24 You Complete Me: Complementary and Supplementary Angles 26 Adding and Subtracting Segments and Angles 30 Multiplying and Dividing Angles and Segments 33 X Marks the Spot: Using Vertical Angles 37 Switching It Up with the Transitive and Substitution Properties 39 Solutions for Points, Segments, Lines, Rays, and Angles 42 Part II: Triangles 49 Chapter 3: Triangle Fundamentals and Other Cool Stuff 51 Triangle Types and Triangle Basics 51 Altitudes, Area, and the Super Hero Formula 55 Balancing Things Out with Medians and Centroids 58 Three More Centers of a Triangle 59 The Pythagorean Theorem 64 Pythagorean Triple Triangles 67 Unique Degrees: Two Special Right Triangles 70 Solutions for Triangle Fundamentals and Other Cool Stuff 74 Chapter 4: Congruent Triangles 83 Sizing Up Three Ways to Prove Triangles Congruent 83 Corresponding Parts of Congruent Triangles Are Congruent (CPCTC) 89 Isosceles Rules: If Sides, Then Angles; If Angles, Then Sides 93 Two More Ways to Prove Triangles Congruent 96 The Two Equidistance Theorems 99 Solutions for Congruent Triangles 104 Part III: Polygons 113 Chapter 5: Quadrilaterals: Your Fine, Four-Sided Friends 115 Double-Crossers: Transversals and Their Parallel Lines 115 Quadrilaterals: Its a Family Affair 120 Properties of the Parallelogram and the Kite 123 Properties of Rhombuses, Rectangles, and Squares 127 Properties of Trapezoids and Isosceles Trapezoids 130 Proving That a Quadrilateral is a Parallelogram or a Kite 132 Proving That a Quadrilateral is a Rhombus, Rectangle, or Square 136 Solutions for Quadrilaterals: Your Fine, Four-Sided Friends 139 Chapter 6: Area, Angles, and the Many Sides of Polygon Geometry 151 Square Units: Finding the Area of Quadrilaterals 151 A Standard Formula for the Area of Regular Polygons 155 More Fantastically Fun Polygon Formulas 157 Solutions for Area, Angles, and the Many Sides of Polygon Geometry 160 Chapter 7: Similarity: Size Doesnt Matter 165 Defining Similarity: The Sincerest Flattery 165 Proving Triangles Similar 168 Corresponding Sides and CSSTP Cats Stalk Silently Then Pounce 172 Similar Rights: The Altitude-on-Hypotenuse Theorem 175 Three More Theorems Involving Proportions 178 Solutions for Similarity: Size Doesnt Matter 183 Part IV: Circles 193 Chapter 8: Circular Reasoning 195 The Segments Within: Radii and Chords 195 Introducing Arcs, Chords, and Central Angles 199 Touching on Radii and Tangents 202 Solutions for Circular Reasoning 206 Chapter 9: Scintillating Circle Formulas 211 Not Quite Coming Full Circle: Area and Perimeter of Circles, Sectors, and Segments 211 Angles, Circles, and Their Connections: The Angle-Arc Theorems and Formulas 214 The Power Theorems That Be 217 Solutions for Scintillating Circle Formulas 221 Part V: 3-D Geometry and Coordinate Geometry 227 Chapter 10: 2-D Stuff Standing Up 229 Lines Perpendicular to Planes: Theyre All Right 229 Parallel, Perpendicular, and Intersecting Lines and Planes 233 S