TEST 174 Elementary Geometry for College Students

4 Quadrilaterals 177

4.1

Properties of a Parallelogram 178 4.2 The Parallelogram and Kite 187 4.3 The Rectangle, Square, and Rhombus 195 4.4 The Trapezoid 204 왘 PERSPECTIVE ON HISTORY: Sketch of Thales 211 왘 PERSPECTIVE ON APPLICATION: Square Numbers as Sums 211 SUMMARY 212 REVIEW EXERCISES 214

CHAPTER 4 TEST 216

5 Similar Triangles 219

5.1

Ratios, Rates, and Proportions 220 5.2 Similar Polygons 227 5.3 Proving Triangles Similar 235

5.4

The Pythagorean Theorem 244 5.5 Special Right Triangles 252 5.6 Segments Divided Proportionally 259 왘 PERSPECTIVE ON HISTORY: Ceva’s Proof 269 왘 PERSPECTIVE ON APPLICATION: An Unusual Application of Similar Triangles 269 SUMMARY 270 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 288 6.3 Line and Segment Relationships in the Circle 299

6.4

Some Constructions and Inequalities for the Circle 309 왘 PERSPECTIVE ON HISTORY: Circumference of the Earth 316 왘 PERSPECTIVE ON APPLICATION: Sum of the Interior Angles of a Polygon 316 SUMMARY 317 REVIEW EXERCISES 319

CHAPTER 6 TEST 321

7 Locus and Concurrence 323

7.1

Locus of Points 324

7.2

Concurrence of Lines 330 7.3 More About Regular Polygons 338 왘 PERSPECTIVE ON HISTORY: The Value of ␲ 345 왘 PERSPECTIVE ON APPLICATION: The Nine-Point Circle 346 SUMMARY 347 REVIEW EXERCISES 349

CHAPTER 7 TEST 350

8 Areas of Polygons and Circles 351

8.1

Area and Initial Postulates 352 8.2 Perimeter and Area of Polygons 363 8.3 Regular Polygons and Area 373 8.4 Circumference and Area of a Circle 379 8.5 More Area Relationships in the Circle 387 왘 PERSPECTIVE ON HISTORY: Sketch of Pythagoras 394 왘 PERSPECTIVE ON APPLICATION: Another Look at the Pythagorean Theorem

394

SUMMARY 396 REVIEW EXERCISES 398

CHAPTER 8 TEST 400

9 Surfaces and Solids 403

9.1

Prisms, Area, and Volume 404 9.2 Pyramids, Area, and Volume 413 9.3 Cylinders and Cones 424 9.4 Polyhedrons and Spheres 433 왘 PERSPECTIVE ON HISTORY: Sketch of René Descartes 443 왘 PERSPECTIVE ON APPLICATION: Birds in Flight 444 SUMMARY 444 REVIEW EXERCISES 446

CHAPTER 9 TEST 447

10 Analytic Geometry 449 10.1 The Rectangular Coordinate System 450 10.2 Graphs of Linear Equations and Slope 458 10.3 Preparing to Do Analytic Proofs 466 10.4 Analytic Proofs 475 10.5 Equations of Lines 480 왘 PERSPECTIVE ON HISTORY: The Banach-Tarski Paradox 488 왘 PERSPECTIVE ON APPLICATION: The Point-of-Division Formulas 489 SUMMARY 490 REVIEW EXERCISES 490

CHAPTER 10 TEST 492

11 Introduction to Trigonometry 495 11.1 The Sine Ratio and Applications 496 11.2 The Cosine Ratio and Applications 504 11.3 The Tangent Ratio and Other Ratios 511 11.4 Applications with Acute Triangles 520 왘 PERSPECTIVE ON HISTORY: Sketch of Plato 529 왘 PERSPECTIVE ON APPLICATION: Radian Measure of Angles 530 SUMMARY 532 REVIEW EXERCISES 532

CHAPTER 11 TEST 534

Glossary 595 Index 599 Appendices 537 APPENDIX A: Algebra Review 537 APPENDIX B: Summary of Constructions, Postulates, Theorems, and Corollaries 563 Answers 571 Selected Exercises and Proofs 571