Geometry workbook for dummies
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書誌事項
Geometry workbook for dummies
Wiley Publishing, c2007
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注記
Includes index
内容説明・目次
内容説明
Make gerometry paractice easy and dun!
Geometry is one of the oldest mathematical subjects in history. Unfortunately, few geometry study guides offer clear explanations, causing many people to get tripped up or lost when trying to solve a proof-even when they know the terms and concepts like the back of their hand. However, this problem can be fixed with practice and some strategies for slicing through all the mumbo-jumbo and getting right to the heart of the proof. Geometry Workbook For Dummies ensures that practice makes perfect, especially when problems are presented without the stiff, formal style that you'd find in your math textbook. Written with a commonsense, street-smart approach, this guide gives you the step-by-step process to solve each proof, along with tips, shortcuts, and mnemonic devices to make sure the solutions stick. It also gives you plenty of room to work out your solutions, providing you with space to breathe and a clear head. This book provides you with the tools you need to solve all types of geometry problems, including:
Congruent triangles
Finding the area, angle, and size of quadrilaterals
Angle-arc theorems and formulas
Touching radii and tangents
Connecting radii and chords
Parallel, perpendicular, and intersecting lines and planes
Slope, distance, and midpoint formulas
Line and circle equations
Handling rotations, reflections, and other transformations
Packed with tons of strategies for solving proofs and a review of key concepts, Geometry Workbook For Dummies is the ultimate study aid for students, parents, and anyone with an interest in the field.
目次
- 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: It's 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 Doesn't 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 Doesn't 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: They're All Right 229 Parallel, Perpendicular, and Intersecting Lines and Planes 233 Solutions for 2-D Stuff Standing Up 238 Chapter 11: Solid Geometry: Digging into Volume and Surface Area 243 Starting with Flat-Top Figures 243 Sharpening Your Skills with Pointy-Top Figures 246 Rounding Out Your Understanding with Spheres 249 Solutions for Solid Geometry 251 Chapter 12: Coordinate Geometry, Courtesy of Descartes 257 Formulas, Schmormulas: Slope, Distance, and Midpoint 257 Mastering Coordinate Proofs with Algebra 260 Using the Equations of Lines and Circles 261 Solutions for Coordinate Geometry, Courtesy of Descartes 264 Chapter 13: Transforming the (Geometric) World: Reflections, Rotations, and Translations 271 Reflections on Mirror Images 271 Les Transformations Geometriques 274 So You Say You Want a Rotation? 276 Working with Glide Reflections 278 Solutions for Transforming the World 281 Part VI: The Part of Tens 285 Chapter 14: Ten (Plus) Incredibly Fantastic Strategies for Doing Proofs 287 Look for Congruent Triangles 287 Try to Find Isosceles Triangles 287 Look for Radii, and Draw More Radii 288 Look for Parallel Lines 288 Make a Game Plan 288 Use All the Givens 288 Check Your If-Then Logic 288 Work Backwards 289 Make Up Numbers for Segments and Angles 289 Think Like a Computer 289 Bonus! Number 11 (Like the Amp in Spinal Tap That Goes Up to 11): Do Something! 290 Chapter 15: Ten Things You Better Know (for Geometry), or Your Name is Mudd 291 The Pythagorean Theorem (the Queen of All Geometry Theorems) 291 Special Right Triangles 291 Area Formulas 292 Sum of Angles 292 Circle Formulas 292 Angle-Arc Theorems 292 Power Theorems 293 Coordinate Geometry Formulas 293 Volume Formulas 293 Surface Area Formulas 294 Index 295
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