## Elementary Geometry for College Students, Seventh Edition

By Daniel C. Alexander and Geralyn M. Koeberlein

**Content:**

Preface ix

Acknowledgments xii

Foreword xiii

Index of Applications xv

Preliminary Concepts 1

P.1 Sets and Geometry 2

P.2 Statements and Reasoning 8

P.3 Informal Geometry and Measurement 16

■■ PERSPECTIVE on History: Our Greek Heritage 25

■■ PERSPECTIVE on Applications: One-to-One Correspondence 26

■■ Summary 26

■■Review Exercises 28

■■ Chapter P Test 30

1 Line and Angle Relationships 31

1.1 Early Definitions and Postulates 32

1.2 Angles and Their Relationships 41

1.3 Introduction to Geometric Proof 49

1.4 Relationships: Perpendicular Lines 56

1.5 The Formal Proof of a Theorem 63

■■ Perspectives on History: The Development of Geometry 69

■■ PERSPECTIVE on Applications: Patterns 70

■■ Summary 71

■■Review Exercises 74

■■ Chapter 1 Test 76

2 Parallel Lines 79

2.1 The Parallel Postulate and Special Angles 80

2.2 Indirect Proof 89

2.3 Proving Lines Parallel 95

2.4 The Angles of a Triangle 101

2.5 Convex Polygons 108

2.6 Symmetry and Transformations 116

■■ PERSPECTIVE on History: Sketch of Euclid 126

■■ PERSPECTIVE on Applications: Non-Euclidean Geometries 126

■■ Summary 128

■■Review Exercises 131

■■ Chapter 2 Test 133

3 Triangles 135

3.1 Congruent Triangles 136

3.2 Corresponding Parts of Congruent Triangles 145

3.3 Isosceles Triangles 153

3.4 Basic Constructions Justified 161

3.5 Inequalities in a Triangle 167

■■ PERSPECTIVE on History: Sketch of Archimedes 174

■■ PERSPECTIVE on Applications: The Geodesic Dome 175

■■ Summary 175

■■Review Exercises 177

■■ Chapter 3 Test 179

4 Quadrilaterals 181

4.1 Properties of a Parallelogram 182

4.2 The Parallelogram and Kite 191

4.3 The Rectangle, Square, and Rhombus 198

4.4 The Trapezoid 206

■■ PERSPECTIVE on History: Sketch of Thales 214

■■ PERSPECTIVE on Applications: Square Number as Sums 214

■■ Summary 215

■■Review Exercises 217

■■ Chapter 4 Test 218

5 Similar Triangles 221

5.1 Ratios, Rates, and Proportions 222

5.2 Similar Polygons 229

5.3 Proving Triangles Similar 237

5.4 The Pythagorean Theorem 246

5.5 Special Right Triangles 254

5.6 Segments Divided Proportionally 261

■■ PERSPECTIVE on History: Ceva’s Proof 269

■■ PERSPECTIVE on Applications: Generating Pythagorean Triples 270

■■ Summary 271

■■Review Exercises 273

■■ Chapter 5 Test 275

6 Circles 277

6.1 Circles and Related Segments and Angles 278

6.2 More Angle Measures in the Circle 287

6.3 Line and Segment Relationships in the Circle 297

6.4 Some Constructions and Inequalities for the Circle 306

■■ PERSPECTIVE on History: Circumference of the Earth 312

■■ PERSPECTIVE on Applications: Sum of Interior Angles of a Polygon 313

■■ Summary 313

■■Review Exercises 315

■■ Chapter 6 Test 317

7 Locus and Concurrence 319

7.1 Locus of Points 320

7.2 Concurrence of Lines 329

7.3 More About Regular Polygons 337

■■ PERSPECTIVE on History: The Value of p 344

■■ PERSPECTIVE on Applications: The Nine-Point Circle 345

■■ Summary 346

■■Review Exercises 348

■■ Chapter 7 Test 349

8 Areas of Polygons and Circles 351

8.1 Area and Initial Postulates 352

8.2 Perimeter and Area of Polygons 362

8.3 Regular Polygons and Area 372

8.4 Circumference and Area of a Circle 378

8.5 More Area Relationships in the Circle 385

■■ PERSPECTIVE on History: Sketch of Pythagoras 391

■■ PERSPECTIVE on Applications: Another Look at the Pythagorean Theorem 392

■■ Summary 393

■■Review Exercises 395

■■ Chapter 8 Test 397

9 Surfaces and Solids 399

9.1 Prisms, Area, and Volume 400

9.2 Pyramids, Area, and Volume 409

9.3 Cylinders and Cones 419

9.4 Polyhedrons and Spheres 429

■■ PERSPECTIVE on History: Sketch of René Descartes 438

■■ PERSPECTIVE on Application S: Birds in Flight 439

■■ Summary 439

■■ Review Exercises 440

■■ Chapter 9 Test 442

10 Analytic Geometry 443

10.1 The Rectangular Coordinate System 444

10.2 Graphs of Linear Equations and Slope 452

10.3 Preparing to Do Analytic Proofs 460

10.4 Analytic Proofs 468

10.5 **Equations of Lines** 474

10.6 The Three-Dimensional Coordinate System 481

■■ PERSPECTIVE on History: The Banach-Tarski Paradox 492

■■ PERSPECTIVE on Application S: The Point-of-Division Formulas 492

■■ Summary 493

■■ Review Exercises 494

■■ Chapter 10 Test 495

11 Introduction to **Trigonometry** 497

11.1 The Sine Ratio and Applications 498

11.2 The Cosine Ratio and Applications 506

11.3 The Tangent Ratio and Other Ratios 512

11.4 Applications with Acute Triangles 521

■■ PERSPECTIVE on History: Sketch of Plato 529

■■ PERSPECTIVE on Application S: Radian Measure of Angles 530

■■ Summary 531

■■ Review Exercises 532

■■ Chapter 11 Test 533

Appendices

APPENDIX A: Algebra Review 535

APPENDIX B: Summary of Constructions, Postulates,

Theorems, Lemmas, and Corollaries 563

Answers

Selected Exercises and Proofs 569

Glossary 591

Index 595