Description
Book SynopsisAccording to the National Assessment of Education Progress, almost six out of ten students take geometry. This workbook features a variety of hands--on geometry problems so students can apply the principles and test their understanding of complex concepts, terms, theorems, proofs, and techniques.
Table of ContentsIntroduction 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 Géométriques 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
