# Geometry: The Easy Way

## Paperback(Fifth Edition)

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## Overview

This new edition in Barron's Easy Way Series contains everything students need to prepare for a geometry class. Geometry: The Easy Way provides key content review and practice exercises to help students learn geometry the easy way.

Topics covered in this detailed review of algebra include the "how" and "why" of geometry, with examples, exercises, and solutions throughout, plus hundreds of drawings, graphs, and tables.

Practice questions in each chapter help students develop their skills and gauge their progress. Visual references including charts, graphs, diagrams, instructive illustrations, and icons help engage students and reinforce important concepts.

The previous edition of this book was titled E-Z Geometry.

## Product Details

ISBN-13: 9781438012117 Barrons Educational Series 09/03/2019 Barron's Easy Way Fifth Edition 528 413,834 9.90(w) x 6.90(h) x 1.00(d)

## About the Author

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's created his own study guides.

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

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

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