Let's Review Regents: Geometry Revised Edition

by Barron's Educational Series, Andre, Ph.D. Castagna Ph.D.

Overview

Barron's Let's Review Regents: Geometry gives students the step-by-step review and practice they need to prepare for the Regents exam. This updated edition is an ideal companion to high school textbooks and covers all Geometry topics prescribed by the New York State Board of Regents.

This edition includes:

• Two actual Regents exams in Geometry, plus answer keys for each test
• Review and practice problems for all topics on the exam, including the language of geometry, basic geometric relationships (parallel lines, polygons, and triangle relationships), constructions, an introduction to geometric proof transformations, triangle congruence, similarity and right triangle trigonometry, parallelograms, circles and arcs, coordinate geometry and proofs on the coordinate plane, and volume (modeling 3-D shapes in practice applications)

 

Product Details

ISBN-13:	9781506266299
Publisher:	Barrons Educational Services
Publication date:	01/05/2021
Series:	Barron's New York Regents
Pages:	608
Sales rank:	286,233
Product dimensions:	5.90(w) x 8.90(h) x 1.40(d)
Age Range:	14 - 17 Years

About the Author

About the Publisher
In the 1930s, Manuel H. Barron opened a bookstore in Brooklyn, New York. 

People from the community asked Mr. Barron about books that might be available to help their children study for the New York State Regents exams. After realizing there wasn't anything available, Mr. Barron created his own study guides.

80 years later, Barron's has helped millions of people prepare for their next step.

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