Painless Geometry

by Lynette Long Ph.D.

Overview

Whether you’re a student or an adult looking to refresh your knowledge, Barron’s Painless Geometry provides review and practice in an easy, step-by-step format.

An essential resource for:

• Virtual Learning
• Homeschool
• Learning pods
• Supplementing classes/in-person learning

Inside you’ll find:

• Comprehensive coverage of geometry, including characteristics of distinct shapes, relationships between parallel and perpendicular lines, geometric principles that can solve real-world problems, and much more   
• Diagrams, charts, instructive math illustrations, proofs, and experiments   
• Painless tips, common pitfalls, and math talk boxes that translate complex “math speak” into easy-to-understand language   
• Brain Tickler quizzes and answers throughout each chapter to test your progress

Product Details

ISBN-13:	9781506268040
Publisher:	Barrons Educational Services
Publication date:	09/01/2020
Series:	Barron's Painless
Edition description:	Fourth Edition
Pages:	320
Sales rank:	242,619
Product dimensions:	5.90(w) x 8.90(h) x 0.80(d)
Age Range:	11 - 14 Years

About the Author

About the Author
Lynette Long, Ph.D. is a math education expert. She is a former elementary and middle school principal, high school mathematics teacher, and college professor at Loyola University in Baltimore, American University in Washington, D.C., and the University of Maryland. Long has taught more than twenty different courses in the areas of education and mathematics and has published more than twenty-five books.

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

How to Use This Book vii

Chapter 1 A Painless Beginning 1

Undefined Terms 1

Some Defined Terms 3

More Defined Terms 5

Postulates 7

Theorems 8

Conditional Statements 9

Geometric Proofs 9

Geometric Symbols 11

Brain Ticklers-The Answers 14

Chapter 2 Angles 15

Measuring Angles 18

Angle Addition 22

Classifying Angles 23

Angle Pairs 25

Angle Congruence 30

Word Problems 32

Brain Ticklers-The Answers 34

Chapter 3 Parallel and Perpendicular Lines 37

Vertical Angles 39

Perpendicular Lines 40

Parallel Lines 44

More on Parallel Lines 48

Brain Ticklers-The Answers 55

Chapter 4 Triangles 57

Interior Angles 57

Exterior Angles 62

Types of Triangles 67

More Types of Triangles 70

Perimeter of a Triangle 76

Area of a Triangle 77

The Pythagorean Theorem 80

Pythagorean Triples 82

30-60-90-Degree Triangles 84

45-45-90-Degree Triangles 88

Brain Ticklers-The Answers 92

Chapter 5 Similar and Congruent Triangles 97

Triangle Parts 97

Triangle Midpoints 98

Similar Triangles 103

Right Triangle Proportions Theorem 105

Congruent Triangles 110

Brain Ticklers-The Answers 119

Chapter 6 Quadrilaterals 121

Trapezoids 121

Isosceles Trapezoids 125

Parallelograms 128

Rhombuses 133

Rectangles 135

Squares 137

Brain Ticklers-The Answers 142

Chapter 7 Polygons 145

Regular and Irregular Polygons 146

Convex and Concave Polygons 146

Sides and Angles of Polygons 147

Exterior Angles of Polygons 151

Inscribed and Circumscribed Polygons 155

Brain Ticklers-The Answers 157

Chapter 8 Circles 159

Radius and Diameter 160

Regions of a Circle 162

Pi 164

Circumference 165

Area of a Circle 166

Degrees in a Circle 170

Chords, Tangents, and Secants 172

Arcs 174

Measuring Arcs 176

Angles and Circles 181

Brain Ticklers-The Answers 191

Chapter 9 Perimeter, Area, and Volume 195

It's a Matter of Units 195

Triangles 195

Rectangles 197

Squares 199

Parallelograms 202

Trapezoids 205

Rhombuses 207

Regular Polygons 209

Unusual Shapes 214

Volume 217

Rectangular Solids 218

Cubes 219

Cylinders 222

Cones 226

Spheres 227

Brain Ticklers-The Answers 231

Chapter 10 Graphing 235

Graphing Points 236

Quadrants 241

The Midpoint Formula 242

The Distance Formula 245

Graphing a Line by Plotting Points 248

Graphing Horizontal and Vertical Lines 251

The Slope 254

Graphing Using Slope-Intercept 259

Finding the Equation of a Line 263

Two-Point Method 264

Point-Slope Form 266

Parallel and Perpendicular Lines 267

Brain Ticklers-The Answers 272

Chapter 11 Constructions 279

Constructing a Congruent Line Segment 280

Constructing Congruent Angles 281

Bisecting an Angle 283

Constructing an Equilateral Triangle 285

Constructing Parallel Lines 286

Constructing Perpendicular Lines 288

Inscribing a Square in a Circle 289

Brain Ticklers-The Answers 293

Appendix I Glossary 295

Appendix II Key Formulas 301

Index 305