Table of Contents
Preface ix
1 Building a Geometry Vocabulary 1
The Building Blocks of Geometry 2
Definitions and Postulates 6
Inductive Versos Deductive Reasoning 9
The IF … THEN … Sentence Structure 10
Review Exercises for Chapter 1 12
2 Measure and Congruence 15
Measurements of Segments and Angles 16
Betweenness of Points and Rays 18
Congruence 20
Basic Constructions 21
Midpoint and Bisector 24
Diagrams and Drawing Conclusions 26
Properties of Equality and Congruence 27
Additional Properties of Equality 31
The Two-Column Proof Format 33
Review Exercises for Chapter 2 35
3 Angle Pairs and Perpendicular Lines 43
Supplementary and Complementary Angle Pairs 44
Adjacent and Vertical Angle Pairs 46
Theorems Relating to Complementary, Supplementary, and Vertical Angles 48
Definitions and Theorems Relating to Right Angles and Perpendiculars 52
A Word About the Format of a Proof 60
Review Exercises for Chapter 3 61
4 Parallel Lines 65
Planes and Lines 66
Properties of Parallel Lines 68
Converses and Methods of Proving Lines Parallel 75
The Parallel Postulate 78
Review Exercises for Chapter 4 82
5 Angles of a Polygon 89
The Anatomy of a Polygon 90
Angles of a Triangle 92
Exterior Angles of a Triangle 97
Angles of a Polygon 100
Review Exercises for Chapter 5 104
6 Proving Triangles are Congruent 109
Correspondences and Congruent Triangles 110
Proving Triangles Congruent: SSS, SAS, and ASA Postulates 113
Proving Overlapping Triangles Congruent 119
Proving Triangles Congruent: AAS and Hy-Leg Methods 122
When Two Triangles Are NOT Congruent 126
Review Exercises for Chapter 6 128
7 Applying Congruent Triangles 133
Using Congruent Triangles to Prove Segments and Angles Congruent 134
Using Congruent Triangles to Prove Special Properties of Lines 137
Classifying Triangles and Special Segments 139
The Isosceles Triangle 141
Double Congruence Proofs 146
Review Exercises for Chapter 7 148
Cumulative Review Exercises: Chapters 1-7 155
8 Transformation Geometry 159
Terms and Notation 160
Congruence Transformations 161
Classifying Isometries 168
Size Transformations 168
Types of Symmetry 171
Transformations in the Coordinate Plane 173
Composing Transformations 180
Congruent Proofs Using Transformations 183
Review Exercises for Chapter 8 185
9 Ratio, Proportion, and Similarity 191
Ratio and Proportion 192
Proportions in a Triangle 198
When Are Polygons Similar? 201
Proving Triangles Similar 207
Proving Lengths of Sides of Similar Triangles in Proportion 211
Proving Products of Segment Lengths Equal 215
Applications of Similar Triangles 218
Review Exercises for Chapter 9 220
10 The Right Triangle 227
Proportions in a Right Triangle 228
The Pythagorean Theorem 231
Special Right-Triangle Relationships 236
Trigonometric Ratios 240
Indirect Measurement in a Right Triangle 246
Review Exercises for Chapter 10 251
11 Geometric Inequalities, Indirect Proof, and Concurrencies 255
Some Basic Properties of Inequalities 256
Inequality Relationships in a Triangle 257
Points of Concurrency in a Triangle 259
The Indirect Method of Proof 263
Review Exercises for Chapter 11 267
Cumulative Review Exercises: Chapters 8-11 271
12 Special Quadrilaterals 277
Classifying Quadrilaterals 278
Properties of a Trapezoid 279
Properties of a Parallelogram 282
Properties of Special Parallelograms 286
Proving a Quadrilateral Is a Parallelogram 290
The Isosceles Trapezoid 296
Review Exercises for Chapter 12 301
13 Circles and Angle Measurement 307
The Parts of a Circle 308
Arcs and Central Angles 313
Diameters and Chords 320
Tangents and Secants 323
Angle Measurement: Vertex on the Circle 329
Angle Measurement: Vertex in the Interior of the Circle 337
Angle Measurement: Vertex in the Exterior of the Circle 339
Using Angle-Measurement Theorems 344
Review Exercises for Chapter 13 349
14 Chord, Tangent, and Secant Segments 357
Equidistant Chords 358
Tangents and Circles 361
Similar Triangles and Circles 365
Tangent- and Sec ant-Segment Relationships 368
Circumference and Arc Length 373
Review Exercises for Chapter 14 379
15 Area and Volume 385
Areas of a Rectangle, Square, and Parallelogram 386
Area of a Triangle 390
Comparing Areas 394
Areas of a Circle, Sector, and Segment 397
Geometric Solids 401
Similar Solids 409
Review Exercises for Chapter 15 411
16 Coordinate Geometry 419
Finding Area Using Coordinates 420
The Midpoint and Distance Formulas 423
Partitioning a Line Segment 429
Slope of a Line 432
Equation of a Line 438
Equation of a Circle 444
Proofs Using Coordinates 446
Review Exercises for Chapter 16 450
Cumulative Review Exercises: Chapters 12-16 455
Some Geometric Relationships and Formulas Worth Remembering 461
Glossary 467
Answers to Chapter Exercises 473
Solutions to Cumulative Review Exercises 503
Index 509
