Table of Contents
Preface vii
Chapter 1 The Tools of Geometry 1
1.1 The Building Blocks of Geometry 1
1.2 Basic Relationships Among Points, Lines, and Planes 11
1.3 Brief Review of Algebra Skills 19
Chapter 2 Angle and Segment Relationships 30
2.1 Basic Angle Relationships 30
2.2 Bisectors, Midpoint, and the Addition Postulate 35
2.3 Angles in Polygons 41
2.4 Parallel Lines 47
2.5 Angles and Sides in Triangles 56
Chapter 3 Constructions 67
3.1 Basic Constructions 67
3.2 Constructions that Build on the Basic Constructions 73
3.3 Points of Concurrency, Inscribed Figures, and Circumscribed Figures 78
Chapter 4 Introduction to Proofs 86
4.1 Structure and Strategy of Writing Proofs 86
4.2 Using Key Idea Midpoints, Bisectors, and Perpendicular Lines 88
4.3 Properties of Equality 94
4.4 Using Vertical Angles, Linear Pairs, and Complementary and Supplementary Angles 102
4.5 Using Parallel Lines 108
4.6 Using Triangle Relationships 113
Chapter 5 Transformations and Congruence 121
5.1 Rigid Motion and Similarity Transformations 121
5.2 Properties of Transformations 127
5.3 Transformations in the Coordinate Plane 136
5.4 Symmetry 149
5.5 Compositions of Rigid Motions 154
Chapter 6 Triangle Congruence 159
6.1 The Triangle Congruence Criterion 160
6.2 Proving Triangles Congruent 169
6.3 CPCTC 181
6.4 Proving Congruence by Transformations 188
Chapter 7 Geometry in the Coordinate Plane 193
7.1 Length, Distance, and Midpoint 193
7.2 Perimeter and Area Using Coordinates 202
7.3 Slope and Equations of Lines 208
7.4 Equations of Parallel and Perpendicular Lines 216
7.5 Equations of Lines and Transformations 223
7.6 The Circle 227
Chapter 8 Similar Figures and Trigonometry 235
8.1 Similar Figures 235
8.2 Proving Triangles Similar and Similarity Transformations 245
8.3 Similar Triangle Relationships 257
8.4 Right Triangle Trigonometry 271
Chapter 9 Parallelograms and Trapezoids 289
9.1 Parallelograms 289
9.2 Proofs with Parallelograms 295
9.3 Properties of Special Parallelograms 303
9.4 Trapezoids 311
9.5 Classifying Quadrilaterals and Proofs Involving Special Quadrilaterals 315
9.6 Parallelograms and Transformations 324
Chapter 10 Coordinate Geometry Proofs 330
10.1 Tools and Strategies of Coordinate Geometry Proofs 330
10.2 Parallelogram Proofs 331
10.3 Triangle Proofs 338
Chapter 11 Circles 346
11.1 Definitions, Arcs, and Angles in Circles 346
11.2 Congruent, Parallel, and Perpendicular Chords 360
11.3 Tangents 370
11.4 Angle-Arc Relationships with Chords, Tangents, and Secants 376
11.5 Segment Relationships in Intersecting Chords, Tangents, and Secants 390
11.6 Area, Circumference, and Arc Length 400
Chapter 12 Solids and Modeling 412
12.1 Prisms and Cylinders 412
12.2 Cones, Pyramids, and Spheres 418
12.3 Cross Sections and Solids of Revolution 424
12.4 Proving Volume and Area by Dissection, Limits, and Cavalieri's Principle 431
12.5 Modeling and Design 443
Answers and Solutions to Practice Exercises 455
Glossary of Geometry Terms 490
Summary of Geometric Relationships and Formulas 498
About the Exam 512
Appendix I The Geometry Learning Standards 518
Appendix II Practice and Test-Taking Tips 523
June 2018 Regents Exam 529
June 2019 Regents Exam 557
Index 583
