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.

• Introduction 1About This Book 1Conventions Used in This Book 2How to Use This Book 2Foolish Assumptions 3Icons Used in This Book 3Beyond the Book 4Where to Go from Here 4Part 1: Getting Started with Geometry 5Chapter 1: Introducing Geometry and Geometry Proofs 7What Is Geometry? 7Making the Right Assumptions 8If-Then Logic: If You Bought This Book, Then You Must Love Geometry! 11What’s a Geometry Proof? 12Solutions 15Chapter 2: Points, Segments, Lines, Rays, and Angles 17Hammering Out Basic Definitions 17Looking at Union and Intersection Problems 18Uncovering More Definitions 20Division in the Ranks: Bisection and Trisection 20Perfect Hilarity for Perpendicularity 23You Complete Me: Complementary and Supplementary Angles 25X Marks the Spot: Vertical Angles 26Solutions 28Chapter 3: Your First Geometry Proofs 33Ready to Try Some Proofs? 33Proofs Involving Complementary and Supplementary Angles 34Proofs Involving Adding and Subtracting Segments and Angles 37Proofs Involving Multiplying and Dividing Angles and Segments 42Proofs Involving the Transitive and Substitution Properties 46Solutions 50Part 2: Triangles, Proof and Non-proof Problems 55Chapter 4: Triangle Fundamentals and Other Cool Stuff (No Proofs) 57Triangle Types and Triangle Basics 58Altitudes, Area, and the Super Hero Formula 61Balancing Things Out with Medians and Centroids 65Locating Three More “Centers” of a Triangle 66The Pythagorean Theorem 71Solving Pythagorean Triple Triangles 74Unique Degrees: Two Special Right Triangles 78Solutions 80Chapter 5: Proofs Involving Congruent Triangles 91Sizing Up Three Ways to Prove Triangles Congruent 91Corresponding Parts of Congruent Triangles Are Congruent 97Using Isosceles Triangle Rules: If Sides, Then Angles; If Angles, Then Sides 102Exploring Two More Ways to Prove Triangles Congruent 105Explaining the Two Equidistance Theorems 108Solutions 113Part 3: Polygons, Proof and Non-proof Problems 121Chapter 6: Quadrilaterals: Your Fine, Four-Sided Friends (Including Proofs) 123Double-Crossers: Transversals and Their Parallel Lines 124Quadrilaterals: It’s a Family Affair 128Discovering the Properties of the Parallelogram and the Kite 132Properties of Rhombuses, Rectangles, and Squares 137Unearthing the Properties of Trapezoids and Isosceles Trapezoids 141Proving That a Quadrilateral Is a Parallelogram or a Kite 143Proving That a Quadrilateral Is a Rhombus, Rectangle, or Square 147Solutions 149Chapter 7: Area, Angles, and the Many Sides of Polygon Geometry (No Proofs) 159Square Units: Finding the Area of Quadrilaterals 159The Standard Formula for the Area of Regular Polygons 163More Fantastically Fun Polygon Formulas 165Solutions 168Chapter 8: Similarity: Size Doesn’t Matter (Including Proofs) 175Defining Similarity 176Proving Triangles Similar 179Corresponding Sides and CSSTP — Cats Stalk Silently Then Pounce 183Similar Rights: The Altitude-on-Hypotenuse Theorem 186Discovering Three More Theorems Involving Proportions 190Solutions 195Part 4: Circles, Proof and Non-proof Problems 205Chapter 9: Circular Reasoning (Including Proofs) 207The Segments Within: Radii and Chords 207Introducing Arcs and Central Angles 211Touching on Radii and Tangents 215Solutions 218Chapter 10: Scintillating Circle Formulas (No Proofs) 223Pizzas, Slices, and Crusts: Finding Area and “Perimeter” of Circles, Sectors, and Segments 223Angles, Circles, and Their Connections: The Angle-Arc Theorems and Formulas 226The Power Theorems That Be 230Solutions 233Part 5: 3-d Geometry: Proof and Non-proof Problems 239Chapter 11: 2-D Stuff Standing Up (Including Proofs) 241Lines Perpendicular to Planes: They’re All Right 241Parallel, Perpendicular, and Intersecting Lines and Planes 245Solutions 249Chapter 12: Solid Geometry: Digging into Volume and Surface Area (No Proofs) 253Starting with Flat-Top Figures 253Sharpening Your Skills with Pointy-Top Figures 256Rounding Out Your Understanding with Spheres 259Solutions 261Part 6: Coordinate Geometry, Loci, and Constructions: Proof and Non-proof Problems 269Chapter 13: Coordinate Geometry, Courtesy of Descartes (Including Proofs) 271Formulas, Schmormulas: Slope, Distance, and Midpoint 272Mastering Coordinate Proofs with Algebra 275Using the Equations of Lines and Circles 276Solutions 279Chapter 14: Transforming the (Geometric) World: Reflections, Rotations, and Translations (No Proofs) 285Reflections on Mirror Images 286Lost in Translation 289So You Say You Want a Rotation? 292Working with Glide Reflections 294Solutions 297Chapter 15: Laboring Over Loci and Constructions (No Proofs) 301Tackling Locus Problems 301Compass and Straightedge Constructions 306Solutions 311Chapter 16: Ten Things You Better Know (for Geometry), or Your Name Is Mudd 319The Pythagorean Theorem (the Queen of All Geometry Theorems) 319Special Right Triangles 320Area Formulas 320Sum of Angles 320Circle Formulas 321Angle-Arc Theorems 321Power Theorems 321Coordinate Geometry Formulas 322Volume Formulas 322Surface Area Formulas 322Index 323

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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.

• Introduction 1About This Book 1Conventions Used in This Book 2How to Use This Book 2Foolish Assumptions 3Icons Used in This Book 3Beyond the Book 4Where to Go from Here 4Part 1: Getting Started with Geometry 5Chapter 1: Introducing Geometry and Geometry Proofs 7What Is Geometry? 7Making the Right Assumptions 8If-Then Logic: If You Bought This Book, Then You Must Love Geometry! 11What’s a Geometry Proof? 12Solutions 15Chapter 2: Points, Segments, Lines, Rays, and Angles 17Hammering Out Basic Definitions 17Looking at Union and Intersection Problems 18Uncovering More Definitions 20Division in the Ranks: Bisection and Trisection 20Perfect Hilarity for Perpendicularity 23You Complete Me: Complementary and Supplementary Angles 25X Marks the Spot: Vertical Angles 26Solutions 28Chapter 3: Your First Geometry Proofs 33Ready to Try Some Proofs? 33Proofs Involving Complementary and Supplementary Angles 34Proofs Involving Adding and Subtracting Segments and Angles 37Proofs Involving Multiplying and Dividing Angles and Segments 42Proofs Involving the Transitive and Substitution Properties 46Solutions 50Part 2: Triangles, Proof and Non-proof Problems 55Chapter 4: Triangle Fundamentals and Other Cool Stuff (No Proofs) 57Triangle Types and Triangle Basics 58Altitudes, Area, and the Super Hero Formula 61Balancing Things Out with Medians and Centroids 65Locating Three More “Centers” of a Triangle 66The Pythagorean Theorem 71Solving Pythagorean Triple Triangles 74Unique Degrees: Two Special Right Triangles 78Solutions 80Chapter 5: Proofs Involving Congruent Triangles 91Sizing Up Three Ways to Prove Triangles Congruent 91Corresponding Parts of Congruent Triangles Are Congruent 97Using Isosceles Triangle Rules: If Sides, Then Angles; If Angles, Then Sides 102Exploring Two More Ways to Prove Triangles Congruent 105Explaining the Two Equidistance Theorems 108Solutions 113Part 3: Polygons, Proof and Non-proof Problems 121Chapter 6: Quadrilaterals: Your Fine, Four-Sided Friends (Including Proofs) 123Double-Crossers: Transversals and Their Parallel Lines 124Quadrilaterals: It’s a Family Affair 128Discovering the Properties of the Parallelogram and the Kite 132Properties of Rhombuses, Rectangles, and Squares 137Unearthing the Properties of Trapezoids and Isosceles Trapezoids 141Proving That a Quadrilateral Is a Parallelogram or a Kite 143Proving That a Quadrilateral Is a Rhombus, Rectangle, or Square 147Solutions 149Chapter 7: Area, Angles, and the Many Sides of Polygon Geometry (No Proofs) 159Square Units: Finding the Area of Quadrilaterals 159The Standard Formula for the Area of Regular Polygons 163More Fantastically Fun Polygon Formulas 165Solutions 168Chapter 8: Similarity: Size Doesn’t Matter (Including Proofs) 175Defining Similarity 176Proving Triangles Similar 179Corresponding Sides and CSSTP — Cats Stalk Silently Then Pounce 183Similar Rights: The Altitude-on-Hypotenuse Theorem 186Discovering Three More Theorems Involving Proportions 190Solutions 195Part 4: Circles, Proof and Non-proof Problems 205Chapter 9: Circular Reasoning (Including Proofs) 207The Segments Within: Radii and Chords 207Introducing Arcs and Central Angles 211Touching on Radii and Tangents 215Solutions 218Chapter 10: Scintillating Circle Formulas (No Proofs) 223Pizzas, Slices, and Crusts: Finding Area and “Perimeter” of Circles, Sectors, and Segments 223Angles, Circles, and Their Connections: The Angle-Arc Theorems and Formulas 226The Power Theorems That Be 230Solutions 233Part 5: 3-d Geometry: Proof and Non-proof Problems 239Chapter 11: 2-D Stuff Standing Up (Including Proofs) 241Lines Perpendicular to Planes: They’re All Right 241Parallel, Perpendicular, and Intersecting Lines and Planes 245Solutions 249Chapter 12: Solid Geometry: Digging into Volume and Surface Area (No Proofs) 253Starting with Flat-Top Figures 253Sharpening Your Skills with Pointy-Top Figures 256Rounding Out Your Understanding with Spheres 259Solutions 261Part 6: Coordinate Geometry, Loci, and Constructions: Proof and Non-proof Problems 269Chapter 13: Coordinate Geometry, Courtesy of Descartes (Including Proofs) 271Formulas, Schmormulas: Slope, Distance, and Midpoint 272Mastering Coordinate Proofs with Algebra 275Using the Equations of Lines and Circles 276Solutions 279Chapter 14: Transforming the (Geometric) World: Reflections, Rotations, and Translations (No Proofs) 285Reflections on Mirror Images 286Lost in Translation 289So You Say You Want a Rotation? 292Working with Glide Reflections 294Solutions 297Chapter 15: Laboring Over Loci and Constructions (No Proofs) 301Tackling Locus Problems 301Compass and Straightedge Constructions 306Solutions 311Chapter 16: Ten Things You Better Know (for Geometry), or Your Name Is Mudd 319The Pythagorean Theorem (the Queen of All Geometry Theorems) 319Special Right Triangles 320Area Formulas 320Sum of Angles 320Circle Formulas 321Angle-Arc Theorems 321Power Theorems 321Coordinate Geometry Formulas 322Volume Formulas 322Surface Area Formulas 322Index 323

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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.

• Introduction 1About This Book 1Conventions Used in This Book 2How to Use This Book 2Foolish Assumptions 3Icons Used in This Book 3Beyond the Book 4Where to Go from Here 4Part 1: Getting Started with Geometry 5Chapter 1: Introducing Geometry and Geometry Proofs 7What Is Geometry? 7Making the Right Assumptions 8If-Then Logic: If You Bought This Book, Then You Must Love Geometry! 11What’s a Geometry Proof? 12Solutions 15Chapter 2: Points, Segments, Lines, Rays, and Angles 17Hammering Out Basic Definitions 17Looking at Union and Intersection Problems 18Uncovering More Definitions 20Division in the Ranks: Bisection and Trisection 20Perfect Hilarity for Perpendicularity 23You Complete Me: Complementary and Supplementary Angles 25X Marks the Spot: Vertical Angles 26Solutions 28Chapter 3: Your First Geometry Proofs 33Ready to Try Some Proofs? 33Proofs Involving Complementary and Supplementary Angles 34Proofs Involving Adding and Subtracting Segments and Angles 37Proofs Involving Multiplying and Dividing Angles and Segments 42Proofs Involving the Transitive and Substitution Properties 46Solutions 50Part 2: Triangles, Proof and Non-proof Problems 55Chapter 4: Triangle Fundamentals and Other Cool Stuff (No Proofs) 57Triangle Types and Triangle Basics 58Altitudes, Area, and the Super Hero Formula 61Balancing Things Out with Medians and Centroids 65Locating Three More “Centers” of a Triangle 66The Pythagorean Theorem 71Solving Pythagorean Triple Triangles 74Unique Degrees: Two Special Right Triangles 78Solutions 80Chapter 5: Proofs Involving Congruent Triangles 91Sizing Up Three Ways to Prove Triangles Congruent 91Corresponding Parts of Congruent Triangles Are Congruent 97Using Isosceles Triangle Rules: If Sides, Then Angles; If Angles, Then Sides 102Exploring Two More Ways to Prove Triangles Congruent 105Explaining the Two Equidistance Theorems 108Solutions 113Part 3: Polygons, Proof and Non-proof Problems 121Chapter 6: Quadrilaterals: Your Fine, Four-Sided Friends (Including Proofs) 123Double-Crossers: Transversals and Their Parallel Lines 124Quadrilaterals: It’s a Family Affair 128Discovering the Properties of the Parallelogram and the Kite 132Properties of Rhombuses, Rectangles, and Squares 137Unearthing the Properties of Trapezoids and Isosceles Trapezoids 141Proving That a Quadrilateral Is a Parallelogram or a Kite 143Proving That a Quadrilateral Is a Rhombus, Rectangle, or Square 147Solutions 149Chapter 7: Area, Angles, and the Many Sides of Polygon Geometry (No Proofs) 159Square Units: Finding the Area of Quadrilaterals 159The Standard Formula for the Area of Regular Polygons 163More Fantastically Fun Polygon Formulas 165Solutions 168Chapter 8: Similarity: Size Doesn’t Matter (Including Proofs) 175Defining Similarity 176Proving Triangles Similar 179Corresponding Sides and CSSTP — Cats Stalk Silently Then Pounce 183Similar Rights: The Altitude-on-Hypotenuse Theorem 186Discovering Three More Theorems Involving Proportions 190Solutions 195Part 4: Circles, Proof and Non-proof Problems 205Chapter 9: Circular Reasoning (Including Proofs) 207The Segments Within: Radii and Chords 207Introducing Arcs and Central Angles 211Touching on Radii and Tangents 215Solutions 218Chapter 10: Scintillating Circle Formulas (No Proofs) 223Pizzas, Slices, and Crusts: Finding Area and “Perimeter” of Circles, Sectors, and Segments 223Angles, Circles, and Their Connections: The Angle-Arc Theorems and Formulas 226The Power Theorems That Be 230Solutions 233Part 5: 3-d Geometry: Proof and Non-proof Problems 239Chapter 11: 2-D Stuff Standing Up (Including Proofs) 241Lines Perpendicular to Planes: They’re All Right 241Parallel, Perpendicular, and Intersecting Lines and Planes 245Solutions 249Chapter 12: Solid Geometry: Digging into Volume and Surface Area (No Proofs) 253Starting with Flat-Top Figures 253Sharpening Your Skills with Pointy-Top Figures 256Rounding Out Your Understanding with Spheres 259Solutions 261Part 6: Coordinate Geometry, Loci, and Constructions: Proof and Non-proof Problems 269Chapter 13: Coordinate Geometry, Courtesy of Descartes (Including Proofs) 271Formulas, Schmormulas: Slope, Distance, and Midpoint 272Mastering Coordinate Proofs with Algebra 275Using the Equations of Lines and Circles 276Solutions 279Chapter 14: Transforming the (Geometric) World: Reflections, Rotations, and Translations (No Proofs) 285Reflections on Mirror Images 286Lost in Translation 289So You Say You Want a Rotation? 292Working with Glide Reflections 294Solutions 297Chapter 15: Laboring Over Loci and Constructions (No Proofs) 301Tackling Locus Problems 301Compass and Straightedge Constructions 306Solutions 311Chapter 16: Ten Things You Better Know (for Geometry), or Your Name Is Mudd 319The Pythagorean Theorem (the Queen of All Geometry Theorems) 319Special Right Triangles 320Area Formulas 320Sum of Angles 320Circle Formulas 321Angle-Arc Theorems 321Power Theorems 321Coordinate Geometry Formulas 322Volume Formulas 322Surface Area Formulas 322Index 323

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