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Don't be a square! Strengthen your geometrical skills Lots of students need extra practice to master geometry. Thankfully, there's Geometry Workbook For Dummies. Packed with hundreds of practice problems and easy-to-understand concept explanations, this book takes a hands-on approach to showing you the geometric ropes. Inside, you'll find a helpful review of basic terms and concepts, so you can hit the ground running when you get to the more advanced stuff. In classic Dummies style, this workbook offers easy ways to understand theorems, proofs, and other geometry fundamentals. Figure out…mehr
Don't be a square! Strengthen your geometrical skills
Lots of students need extra practice to master geometry. Thankfully, there's Geometry Workbook For Dummies. Packed with hundreds of practice problems and easy-to-understand concept explanations, this book takes a hands-on approach to showing you the geometric ropes. Inside, you'll find a helpful review of basic terms and concepts, so you can hit the ground running when you get to the more advanced stuff. In classic Dummies style, this workbook offers easy ways to understand theorems, proofs, and other geometry fundamentals. Figure out congruent triangles, wrap your mind around angle-arc theorems, connect radii and chords, and get smart about all the core concepts of geometry.
Work through hundreds of practice problems to solidify your geometry know-how
Clear up any confusion with easy-to-understand explanations of all key concepts
Get tips for avoiding common mistakes and improving your test scores
For students or parents looking for a hands-on approach to learning geometry, this is the perfect Dummies guide. It's great resource all on its own, or pair it with Geometry For Dummies for even more effective book learning.
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Autorenporträt
Mark Ryan has more than three decades' experience as a geometry teacher and tutor. He has a gift for mathematics and a gift for explaining it in plain English. He tutors students in all junior high and high school math courses as well as math test prep, and he's the founder of The Math Center on Chicago's North Shore. Ryan is the author of Geometry For Dummies, Geometry Essentials For Dummies, Calculus For Dummies, and several other math books.
Inhaltsangabe
Introduction 1 About This Book 1 Conventions Used in This Book 2 How to Use This Book 2 Foolish Assumptions 3 Icons Used in This Book 3 Beyond the Book 4 Where to Go from Here 4 Part 1: Getting Started with Geometry 5 Chapter 1: Introducing Geometry and Geometry Proofs 7 What Is Geometry? 7 Making the Right Assumptions 8 If-Then Logic: If You Bought This Book, Then You Must Love Geometry! 11 What's a Geometry Proof? 12 Solutions 15 Chapter 2: Points, Segments, Lines, Rays, and Angles 17 Hammering Out Basic Definitions 17 Looking at Union and Intersection Problems 18 Uncovering More Definitions 20 Division in the Ranks: Bisection and Trisection 20 Perfect Hilarity for Perpendicularity 23 You Complete Me: Complementary and Supplementary Angles 25 X Marks the Spot: Vertical Angles 26 Solutions 28 Chapter 3: Your First Geometry Proofs 33 Ready to Try Some Proofs? 33 Proofs Involving Complementary and Supplementary Angles 34 Proofs Involving Adding and Subtracting Segments and Angles 37 Proofs Involving Multiplying and Dividing Angles and Segments 42 Proofs Involving the Transitive and Substitution Properties 46 Solutions 50 Part 2: Triangles, Proof and Non-proof Problems 55 Chapter 4: Triangle Fundamentals and Other Cool Stuff (No Proofs) 57 Triangle Types and Triangle Basics 58 Altitudes, Area, and the Super Hero Formula 61 Balancing Things Out with Medians and Centroids 65 Locating Three More "Centers" of a Triangle 66 The Pythagorean Theorem 71 Solving Pythagorean Triple Triangles 74 Unique Degrees: Two Special Right Triangles 78 Solutions 80 Chapter 5: Proofs Involving Congruent Triangles 91 Sizing Up Three Ways to Prove Triangles Congruent 91 Corresponding Parts of Congruent Triangles Are Congruent 97 Using Isosceles Triangle Rules: If Sides, Then Angles; If Angles, Then Sides 102 Exploring Two More Ways to Prove Triangles Congruent 105 Explaining the Two Equidistance Theorems 108 Solutions 113 Part 3: Polygons, Proof and Non-proof Problems 121 Chapter 6: Quadrilaterals: Your Fine, Four-Sided Friends (Including Proofs) 123 Double-Crossers: Transversals and Their Parallel Lines 124 Quadrilaterals: It's a Family Affair 128 Discovering the Properties of the Parallelogram and the Kite 132 Properties of Rhombuses, Rectangles, and Squares 137 Unearthing the Properties of Trapezoids and Isosceles Trapezoids 141 Proving That a Quadrilateral Is a Parallelogram or a Kite 143 Proving That a Quadrilateral Is a Rhombus, Rectangle, or Square 147 Solutions 149 Chapter 7: Area, Angles, and the Many Sides of Polygon Geometry (No Proofs) 159 Square Units: Finding the Area of Quadrilaterals 159 The Standard Formula for the Area of Regular Polygons 163 More Fantastically Fun Polygon Formulas 165 Solutions 168 Chapter 8: Similarity: Size Doesn't Matter (Including Proofs) 175 Defining Similarity 176 Proving Triangles Similar 179 Corresponding Sides and CSSTP - Cats Stalk Silently Then Pounce 183 Similar Rights: The Altitude-on-Hypotenuse Theorem 186 Discovering Three More Theorems Involving Proportions 190 Solutions 195 Part 4: Circles, Proof and Non-proof Problems 205 Chapter 9: Circular Reasoning (Including Proofs) 207 The Segments Within: Radii and Chords 207 Introducing Arcs and Central Angles 211 Touching on Radii and Tangents 215 Solutions 218 Chapter 10: Scintillating Circle Formulas (No Proofs) 223 Pizzas, Slices, and Crusts: Finding Area and "Perimeter" of Circles, Sectors, and Segments 223 Angles, Circles, and Their Connections: The Angle-Arc Theorems and Formulas 226 The Power Theorems That Be 230 Solutions 233 Part 5: 3-d Geometry: Proof and Non-proof Problems 239 Chapter 11: 2-D Stuff Standing Up (Including Proofs) 241 Lines Perpendicular to Planes: They're All Right 241 Parallel, Perpendicular, and Intersecting Lines and Planes 245 Solutions 249 Chapter 12: Solid Geometry: Digging into Volume and Surface Area (No Proofs) 253 Starting with Flat-Top Figures 253 Sharpening Your Skills with Pointy-Top Figures 256 Rounding Out Your Understanding with Spheres 259 Solutions 261 Part 6: Coordinate Geometry, Loci, and Constructions: Proof and Non-proof Problems 269 Chapter 13: Coordinate Geometry, Courtesy of Descartes (Including Proofs) 271 Formulas, Schmormulas: Slope, Distance, and Midpoint 272 Mastering Coordinate Proofs with Algebra 275 Using the Equations of Lines and Circles 276 Solutions 279 Chapter 14: Transforming the (Geometric) World: Reflections, Rotations, and Translations (No Proofs) 285 Reflections on Mirror Images 286 Lost in Translation 289 So You Say You Want a Rotation? 292 Working with Glide Reflections 294 Solutions 297 Chapter 15: Laboring Over Loci and Constructions (No Proofs) 301 Tackling Locus Problems 301 Compass and Straightedge Constructions 306 Solutions 311 Chapter 16: Ten Things You Better Know (for Geometry), or Your Name Is Mudd 319 The Pythagorean Theorem (the Queen of All Geometry Theorems) 319 Special Right Triangles 320 Area Formulas 320 Sum of Angles 320 Circle Formulas 321 Angle-Arc Theorems 321 Power Theorems 321 Coordinate Geometry Formulas 322 Volume Formulas 322 Surface Area Formulas 322 Index 323
Introduction 1 About This Book 1 Conventions Used in This Book 2 How to Use This Book 2 Foolish Assumptions 3 Icons Used in This Book 3 Beyond the Book 4 Where to Go from Here 4 Part 1: Getting Started with Geometry 5 Chapter 1: Introducing Geometry and Geometry Proofs 7 What Is Geometry? 7 Making the Right Assumptions 8 If-Then Logic: If You Bought This Book, Then You Must Love Geometry! 11 What's a Geometry Proof? 12 Solutions 15 Chapter 2: Points, Segments, Lines, Rays, and Angles 17 Hammering Out Basic Definitions 17 Looking at Union and Intersection Problems 18 Uncovering More Definitions 20 Division in the Ranks: Bisection and Trisection 20 Perfect Hilarity for Perpendicularity 23 You Complete Me: Complementary and Supplementary Angles 25 X Marks the Spot: Vertical Angles 26 Solutions 28 Chapter 3: Your First Geometry Proofs 33 Ready to Try Some Proofs? 33 Proofs Involving Complementary and Supplementary Angles 34 Proofs Involving Adding and Subtracting Segments and Angles 37 Proofs Involving Multiplying and Dividing Angles and Segments 42 Proofs Involving the Transitive and Substitution Properties 46 Solutions 50 Part 2: Triangles, Proof and Non-proof Problems 55 Chapter 4: Triangle Fundamentals and Other Cool Stuff (No Proofs) 57 Triangle Types and Triangle Basics 58 Altitudes, Area, and the Super Hero Formula 61 Balancing Things Out with Medians and Centroids 65 Locating Three More "Centers" of a Triangle 66 The Pythagorean Theorem 71 Solving Pythagorean Triple Triangles 74 Unique Degrees: Two Special Right Triangles 78 Solutions 80 Chapter 5: Proofs Involving Congruent Triangles 91 Sizing Up Three Ways to Prove Triangles Congruent 91 Corresponding Parts of Congruent Triangles Are Congruent 97 Using Isosceles Triangle Rules: If Sides, Then Angles; If Angles, Then Sides 102 Exploring Two More Ways to Prove Triangles Congruent 105 Explaining the Two Equidistance Theorems 108 Solutions 113 Part 3: Polygons, Proof and Non-proof Problems 121 Chapter 6: Quadrilaterals: Your Fine, Four-Sided Friends (Including Proofs) 123 Double-Crossers: Transversals and Their Parallel Lines 124 Quadrilaterals: It's a Family Affair 128 Discovering the Properties of the Parallelogram and the Kite 132 Properties of Rhombuses, Rectangles, and Squares 137 Unearthing the Properties of Trapezoids and Isosceles Trapezoids 141 Proving That a Quadrilateral Is a Parallelogram or a Kite 143 Proving That a Quadrilateral Is a Rhombus, Rectangle, or Square 147 Solutions 149 Chapter 7: Area, Angles, and the Many Sides of Polygon Geometry (No Proofs) 159 Square Units: Finding the Area of Quadrilaterals 159 The Standard Formula for the Area of Regular Polygons 163 More Fantastically Fun Polygon Formulas 165 Solutions 168 Chapter 8: Similarity: Size Doesn't Matter (Including Proofs) 175 Defining Similarity 176 Proving Triangles Similar 179 Corresponding Sides and CSSTP - Cats Stalk Silently Then Pounce 183 Similar Rights: The Altitude-on-Hypotenuse Theorem 186 Discovering Three More Theorems Involving Proportions 190 Solutions 195 Part 4: Circles, Proof and Non-proof Problems 205 Chapter 9: Circular Reasoning (Including Proofs) 207 The Segments Within: Radii and Chords 207 Introducing Arcs and Central Angles 211 Touching on Radii and Tangents 215 Solutions 218 Chapter 10: Scintillating Circle Formulas (No Proofs) 223 Pizzas, Slices, and Crusts: Finding Area and "Perimeter" of Circles, Sectors, and Segments 223 Angles, Circles, and Their Connections: The Angle-Arc Theorems and Formulas 226 The Power Theorems That Be 230 Solutions 233 Part 5: 3-d Geometry: Proof and Non-proof Problems 239 Chapter 11: 2-D Stuff Standing Up (Including Proofs) 241 Lines Perpendicular to Planes: They're All Right 241 Parallel, Perpendicular, and Intersecting Lines and Planes 245 Solutions 249 Chapter 12: Solid Geometry: Digging into Volume and Surface Area (No Proofs) 253 Starting with Flat-Top Figures 253 Sharpening Your Skills with Pointy-Top Figures 256 Rounding Out Your Understanding with Spheres 259 Solutions 261 Part 6: Coordinate Geometry, Loci, and Constructions: Proof and Non-proof Problems 269 Chapter 13: Coordinate Geometry, Courtesy of Descartes (Including Proofs) 271 Formulas, Schmormulas: Slope, Distance, and Midpoint 272 Mastering Coordinate Proofs with Algebra 275 Using the Equations of Lines and Circles 276 Solutions 279 Chapter 14: Transforming the (Geometric) World: Reflections, Rotations, and Translations (No Proofs) 285 Reflections on Mirror Images 286 Lost in Translation 289 So You Say You Want a Rotation? 292 Working with Glide Reflections 294 Solutions 297 Chapter 15: Laboring Over Loci and Constructions (No Proofs) 301 Tackling Locus Problems 301 Compass and Straightedge Constructions 306 Solutions 311 Chapter 16: Ten Things You Better Know (for Geometry), or Your Name Is Mudd 319 The Pythagorean Theorem (the Queen of All Geometry Theorems) 319 Special Right Triangles 320 Area Formulas 320 Sum of Angles 320 Circle Formulas 321 Angle-Arc Theorems 321 Power Theorems 321 Coordinate Geometry Formulas 322 Volume Formulas 322 Surface Area Formulas 322 Index 323
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