The Complete Idiot's Guide to Geometry

Denise Szecsei

Penguin, 2004 - Mathematics - 376 pages

Geometry is hard. This book makes it easier. You do the math. This is the fourth title in the series designed to help high school and college students through a course they'd rather not be taking. A non-intimidating, easy- to-understand companion to their textbook, this book takes students through the standard curriculum of topics, including proofs, polygons, coordinates, topology, and much more.

Contents

• The Foundation: 1
• What Is Geometry Anyway?: 3
• Whats the Point?: 4
• Getting Into Shape: 5
• Learning How to Write Proofs: 6
• And the Winner Is Euclid: 7
• A Goliath Mathematician: 9
• Can I Really Learn This?: 10
• Lets Do Algebra: 13
• Long Lost Relations: 14
• Properties of Equality: 15
• Reflexive Symmetric and Transitive Properties: 16
• Algebraic Properties of Equality: 17
• The Square Root Property of Equality: 19
• Properties of Inequality: 20
• Is It an Equivalence Relation?: 21
• An Additional Additive Property: 22
• Building Blocks: 25
• Coming to Terms: 26
• Lines: 28
• Line Segments: 29
• Segment Length: 30
• A New Relation: 31
• Segment Addition: 32
• Rays: 33
• Planes: 34
• Theres Always an Angle: 37
• Whats in a Name?: 38
• Are You My Type? The Basic Angle Classifications: 40
• Angle Addition: 41
• How Do Angles Relate? Classifying Pairs of Angles: 42
• Congruent Angles: 43
• Complementary and Supplementary Angles: 44
• A First Look at Proving Angle Congruence: 46
• Lines and the Angles They Form: 49
• Linear Interactions: 50
• Perpendicular Lines: 52
• Euclids 5th: 55
• Transversals and the New Angle Pairs: 57
• A Polygon Is a ManySided Thing: 59
• Coming to Terms with the Terminology: 60
• Naming Conventions and Classifications: 63
• The Interior Angles: 64
• Regular Polygons: 67
• Introducing Proofs: 71
• Logic Rules for Arguing: 73
• Inductive Reasoning: 74
• Elementary My Dear Watson: 75
• Logical Constructions and Truth Tables: 76
• Conjunction: 77
• Disjunction: 78
• Implication or Conditional: 79
• Logical Equivalence and Tautology: 81
• Taking the Burden out of Proofs: 85
• The Law of Detachment: 86
• The Importance of Being Direct: 87
• The Advantage of Being Indirect: 89
• Use It or Lose It: 90
• What Should You Bring to a Formal Proof?: 92
• Proving Segment and Angle Relationships: 97
• Exploring Midpoints: 98
• How Many Midpoints Are There?: 99
• Proving Angles Are Congruent: 101
• Using and Proving Angle Complements: 102
• Using and Proving Angle Supplements: 105
• Proving Relationships Between Lines: 109
• Proofs Involving Perpendicular Lines: 110
• Lets Get Parallel: 112
• Proofs About Alternate Angles: 113
• Parallel Lines and Supplementary Angles: 115
• Using Parallelism to Prove Perpendicularity: 116
• Proving Lines Are Parallel: 117
• Piecing Together Triangles and Quadrilaterals: 123
• Twos Company Threes a Triangle: 125
• A Formal Introduction: 126
• Sums of Interior Angles Are Cooking at 180: 128
• Exterior Angle Relationships: 130
• Size Matters So Lets Measure: 132
• The Pythagorean Theorem: 134
• The Triangle Inequality: 135
• Congruent Triangles: 139
• CPOCTAC: 140
• The SSS Postulate: 141
• The SAS Postulate: 142
• The ASA Postulate: 144
• The AAS Theorem: 145
• The HL Theorem for Right Triangles: 146
• Proving Segments and Angles Are Congruent: 149
• Proving Lines Are Parallel: 150
• Similar Triangles: 155
• Ratio Proportion and Geometric Means: 156
• Properties of Similar Triangles: 159
• The Big Three: 161
• The SAS and SSS Similarity Theorems: 164
• Opening Doors with Similar Triangles: 167
• The Pythagorean Theorem: 168
• Parallel Segments and Segment Proportions: 170
• Three Famous Triangles: 173
• 306090 Triangle: 174
• 454590 Triangle: 176
• Putting Quadrilaterals in the Forefront: 179
• Properties of All Quadrilaterals: 180
• Lets All Fly a Kite: 182
• Properties of Parallelograms: 184
• The Most Popular Parallelograms: 186
• Rhombuses: 187
• Squares: 189
• Area of Parallelograms: 190
• The Pythagorean Theorem again: 191
• Proofs About Quadrilaterals: 195
• When Is a Quadrilateral a Parallelogram?: 196
• Two Pairs of Congruent Sides: 197
• Two Pairs of Congruent Angles: 199
• Bisecting Diagonals: 200
• When Is a Parallelogram a Rectangle?: 201
• When Is a Parallelogram a Rhombus?: 202
• When Is a Parallelogram a Square?: 204
• Going Around in Circles: 207
• Anatomy of a Circle: 209
• Basic Terms: 210
• Arcs: 211
• Pi Anyone?: 215
• Tangents: 217
• From One Theorem Comes Many: 218
• Segments and Angles: 225
• Angles and Chords: 226
• Arcs and Chords: 227
• Radii and Chords: 229
• Putting the Pieces Together: 233
• Circular Arguments: 237
• Angles and Arcs: 238
• Similarity: 241
• Parallel Chords and Arcs: 245
• Putting Your Problems Behind You: 247
• The Unit Circle and Trigonometry: 251
• The Tangent Ratio: 252
• The Sine Ratio: 255
• The Cosine Ratio: 257
• And the Rest: 259
• How Does This Relate to the Unit Circle?: 261
• Where Can We Go from Here?: 267
• The Next Dimension Surfaces and Solids: 269
• Prisms: 270
• Pyramids: 273
• Cylinders and Cones: 274
• Polyhedra: 276
• Spheres: 277
• Platonic Solids: 278
• Under Construction: 281
• Tools of the Trade: 282
• Compass: 283
• Bisection: 284
• Bisecting Angles: 285
• Constructing Lines: 287
• Parallel Lines: 289
• Constructing Quadrilaterals: 290
• Parallelograms: 291
• Squares: 292
• When Geometry and Algebra Intersect: 293
• The Cartesian Coordinate System: 294
• Finding Horizontal and Vertical Distances: 295
• The Pythagorean Theorem Goes the Distance: 296
• The Midpoint Formula: 297
• Finding Equations of Lines: 298
• The PointSlope Formula: 300
• The Secret Lives of Parallel and Perpendicular Lines: 301
• A Picture Is Worth a Thousand Words: 302
• Whose Geometry Is It Anyway?: 305
• NonEuclidean Geometry: 306
• Saddle Up: 307
• Spherical Geometry: 309
• TaxiCab Geometry: 310
• Max Geometry: 312
• How Many Shapes Can a Circle Have?: 313
• Transformations: 317
• Isometrics: 318
• Translations: 319
• Reflections: 320
• Rotations: 322
• Glide Reflections: 324
• Dilations: 325
• Symmetry: 326
• Answer Key: 331
• Postulates and Theorems: 351
• Formulas: 357
• Glossary: 359
• Index: 367

About the author

Denise Szecsei, Ph.D., is an assistant professor of mathematics at Stetson University where she teaches finite mathematics, mathematical modeling, and geometry, as well as a variety of liberal arts mathematics classes. Professor Szecsei developed a geometry class for liberal arts students and elementary education majors and has taught this class over the last three years, giving her firsthand knowledge of how to explain the concepts of geometry to those whose career paths will likely have little to do with the subject.

Bibliographic information

• Title: The Complete Idiot's Guide to Geometry; Complete Idiot's Guide to
• Author: Denise Szecsei
• Edition: illustrated
• Publisher: Penguin, 2004
• ISBN: 1592571832, 9781592571833
• Length: 376 pages
• Subjects: Mathematics / Geometry / General