Table of Contents
How to Use This Book vii
Chapter 1 A Painless Beginning 1
Undefined Terms 1
Some Defined Terms 3
More Defined Terms 5
Postulates 7
Theorems 8
Conditional Statements 9
Geometric Proofs 9
Geometric Symbols 11
Brain Ticklers-The Answers 14
Chapter 2 Angles 15
Measuring Angles 18
Angle Addition 22
Classifying Angles 23
Angle Pairs 25
Angle Congruence 30
Word Problems 32
Brain Ticklers-The Answers 34
Chapter 3 Parallel and Perpendicular Lines 37
Vertical Angles 39
Perpendicular Lines 40
Parallel Lines 44
More on Parallel Lines 48
Brain Ticklers-The Answers 55
Chapter 4 Triangles 57
Interior Angles 57
Exterior Angles 62
Types of Triangles 67
More Types of Triangles 70
Perimeter of a Triangle 76
Area of a Triangle 77
The Pythagorean Theorem 80
Pythagorean Triples 82
30-60-90-Degree Triangles 84
45-45-90-Degree Triangles 88
Brain Ticklers-The Answers 92
Chapter 5 Similar and Congruent Triangles 97
Triangle Parts 97
Triangle Midpoints 98
Similar Triangles 103
Right Triangle Proportions Theorem 105
Congruent Triangles 110
Brain Ticklers-The Answers 119
Chapter 6 Quadrilaterals 121
Trapezoids 121
Isosceles Trapezoids 125
Parallelograms 128
Rhombuses 133
Rectangles 135
Squares 137
Brain Ticklers-The Answers 142
Chapter 7 Polygons 145
Regular and Irregular Polygons 146
Convex and Concave Polygons 146
Sides and Angles of Polygons 147
Exterior Angles of Polygons 151
Inscribed and Circumscribed Polygons 155
Brain Ticklers-The Answers 157
Chapter 8 Circles 159
Radius and Diameter 160
Regions of a Circle 162
Pi 164
Circumference 165
Area of a Circle 166
Degrees in a Circle 170
Chords, Tangents, and Secants 172
Arcs 174
Measuring Arcs 176
Angles and Circles 181
Brain Ticklers-The Answers 191
Chapter 9 Perimeter, Area, and Volume 195
It's a Matter of Units 195
Triangles 195
Rectangles 197
Squares 199
Parallelograms 202
Trapezoids 205
Rhombuses 207
Regular Polygons 209
Unusual Shapes 214
Volume 217
Rectangular Solids 218
Cubes 219
Cylinders 222
Cones 226
Spheres 227
Brain Ticklers-The Answers 231
Chapter 10 Graphing 235
Graphing Points 236
Quadrants 241
The Midpoint Formula 242
The Distance Formula 245
Graphing a Line by Plotting Points 248
Graphing Horizontal and Vertical Lines 251
The Slope 254
Graphing Using Slope-Intercept 259
Finding the Equation of a Line 263
Two-Point Method 264
Point-Slope Form 266
Parallel and Perpendicular Lines 267
Brain Ticklers-The Answers 272
Chapter 11 Constructions 279
Constructing a Congruent Line Segment 280
Constructing Congruent Angles 281
Bisecting an Angle 283
Constructing an Equilateral Triangle 285
Constructing Parallel Lines 286
Constructing Perpendicular Lines 288
Inscribing a Square in a Circle 289
Brain Ticklers-The Answers 293
Appendix I Glossary 295
Appendix II Key Formulas 301
Index 305
