| How to Use This Book | vii |
| The Tools of Geometry | 1 |
| The Building Blocks of Geometry | 1 |
| Basic Relationships Among Points, Lines, and Planes | 11 |
| Brief Review of Algebra Skills | 19 |
| Angle and Segment Relationships | 30 |
| Basic Angle Relationships | 30 |
| Bisectors, Midpoint, and the Addition Postulate | 35 |
| Angles in Polygons | 41 |
| Parallel Lines | 47 |
| Angles and Sides in Triangles | 56 |
| Triangle Inequality Theorem | 67 |
| Constructions | 70 |
| Basic Constructions | 70 |
| Constructions that Build on the Basic Constructions | 76 |
| Points of Concurrency Inscribed Figures, and Circumscribed Figures | 81 |
| Introduction to Proofs | 89 |
| Structure and Strategy of Writing Proofs | 89 |
| Using Key Idea Midpoints, Bisectors, and Perpendicular Lines | 91 |
| Properties of Equality | 97 |
| Using Vertical Angles, Linear Pairs, and Complementary and Supplementary Angles | 105 |
| Using Parallel Lines | 111 |
| Using Triangle Relationships | 116 |
| Transformations and Congruence | 124 |
| Rigid Motions, Similarity Transformations, and Stretches | 124 |
| Properties of Transformations | 131 |
| Transformations in the Coordinate Plane | 140 |
| Symmetry | 155 |
| Compositions of Rigid Motions | 160 |
| Triangle Congruence | 165 |
| The Triangle Congruence Criterion | 166 |
| Proving Triangles Congruent | 175 |
| CPCTC | 187 |
| Proving Congruence by Transformations | 194 |
| Geometry in the Coordinate Plane | 199 |
| Length, Distance, and Midpoint | 199 |
| Perimeter and Area Using Coordinates | 208 |
| Slope and Equations of Lines | 214 |
| Equations of Parallel and Perpendicular Lines | 222 |
| Equations of Lines and Transformations | 229 |
| The Circle | 233 |
| Similar Figures and Trigonometry | 241 |
| Similar Figures | 241 |
| Proving Triangles Similar and Similarity Transformations | 251 |
| Similar Triangle Relationships | 263 |
| Right Triangle Trigonometry | 277 |
| Sine Formula for Area of a Triangle | 295 |
| Special Right Triangles | 298 |
| Parallelograms and Trapezoids | 303 |
| Parallelograms | 303 |
| Proofs with Parallelograms | 309 |
| Properties of Special Parallelograms | 317 |
| Trapezoids | 325 |
| Classifying Quadrilaterals and Proofs Involving Special Quadrilaterals | 329 |
| Parallelograms and Transformations | 338 |
| Coordinate Geometry Proofs | 344 |
| Tools and Strategies of Coordinate Geometry Proofs | 344 |
| Parallelogram Proofs | 345 |
| Triangle Proofs | 352 |
| Circles | 360 |
| Definitions, Arcs, and Angles in Circles | 360 |
| Congruent, Parallel, and Perpendicular Chords | 374 |
| Tangents | 384 |
| Angle-Arc Relationships with Chords, Tangents, and Secants | 390 |
| Segment Relationships in Intersecting Chords, Tangents, and Secants | 404 |
| Area, Circumference, and Arc Length | 414 |
| Solids and Modeling | 426 |
| Prisms and Cylinders | 426 |
| Cones, Pyramids, and Spheres | 432 |
| Cross Sections and Solids of Revolution | 438 |
| Modeling and Design | 445 |
| About the Exam and Strategies | 457 |
| Test Layout | 457 |
| Calculator, Compass, Straightedge, Pen, and Pencil | 458 |
| Preparing for the Exam | 461 |
| Test-Taking Strategies | 461 |
| On Test Day | 463 |
| Answers and Solutions to Practice Exercises | 464 |
| Glossary of Geometry Terms | 498 |
| The Geometry Regents Exam | |
| June 2019 Exam | 506 |
| Answer Key | 529 |
| Sample 2025 Exam | 530 |
| Answer Key | 555 |
| Index | 557 |
| Table of Contents provided by Ingram Syndetics. All Rights Reserved. |
