Elementary Geometry for College Students, (5th Edition)

Front Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Contents......Page 9
Preface......Page 13
Foreword......Page 17
Index of Applications......Page 19
1: Line and Angle Relationships......Page 21
 1.1 Sets, Statements, and Reasoning......Page 22
 1.2 Informal Geometry and Measurement......Page 30
 1.3 Early Definitions and Postulates......Page 41
 1.4 Angles and Their Relationships......Page 50
 1.5 Introduction to Geometric Proof......Page 59
 1.6 Relationships: Perpendicular Lines......Page 66
 1.7 The Formal Proof of a Theorem......Page 73
 PERSPECTIVE ON APPLICATION: Patterns......Page 80
 Summary......Page 82
 Review Exercises......Page 85
 Chapter 1 Test......Page 88
2: Parallel Lines......Page 91
 2.1 The Parallel Postulate and Special Angles......Page 92
 2.2 Indirect Proof......Page 100
 2.3 Proving Lines Parallel......Page 106
 2.4 The Angles of a Triangle......Page 112
 2.5 Convex Polygons......Page 119
 2.6 Symmetry and Transformations......Page 127
 PERSPECTIVE ON APPLICATION: Non-Euclidean Geometrics......Page 138
 Summary......Page 140
 2 Review Exercises......Page 143
 Chapter 2 Test......Page 145
3: Triangles......Page 147
 3.1 Congruent Triangles......Page 148
 3.2 Corresponding Parts of Congruent Triangles......Page 158
 3.3 Isosceles Triangles......Page 165
 3.4 Basic Constructions Justified......Page 174
 3.5 Inequalities in a Triangle......Page 179
 PERSPECTIVE ON APPLICATION: Pascal’s Triangle......Page 188
 Summary......Page 190
 Chapter 3 Test......Page 194
4: Quadrilaterals......Page 197
 4.1 Properties of a Parallelogram......Page 198
 4.2 The Parallelogram and Kite......Page 207
 4.3 The Rectangle, Square, and Rhombus......Page 215
 4.4 The Trapezoid......Page 224
 PERSPECTIVE ON APPLICATION: Square Numbers as Sums......Page 231
 Summary......Page 232
 Review Exercises......Page 234
 Chapter 4 Test......Page 236
5: Similar Triangles......Page 239
 5.1 Ratios, Rates, and Proportions......Page 240
 5.2 Similar Polygons......Page 247
 5.3 Proving Triangles Similar......Page 255
 5.4 The Pythagorean Theorem......Page 264
 5.5 Special Right Triangles......Page 272
 5.6 Segments Divided Proportionally......Page 279
 PERSPECTIVE ON APPLICATION: An Unusual Application of Similar Triangles......Page 289
 Summary......Page 290
 Review Exercises......Page 293
 Chapter 5 Test......Page 295
6: Circles......Page 297
 6.1 Circles and Related Segments and Angles......Page 298
 6.2 More Angle Measures in the Circle......Page 308
 6.3 Line and Segment Relationships in the Circle......Page 319
 6.4 Some Constructions and Inequalities for the Circle......Page 329
 PERSPECTIVE ON APPLICATION: Sum of the interior Angles of a Polygan......Page 336
 Summary......Page 337
 Review Exercises......Page 339
 Chapter 6 Test......Page 341
7: Locus and Concurrence......Page 343
 7.1 Locus of Points......Page 344
 7.2 Concurrence of Lines......Page 350
 7.3 More About Regular Polygons......Page 358
 PERSPECTIVE ON HISTORY: The Value of......Page 365
 PERSPECTIVE ON APPLICATION: The Nine-Point Circle......Page 366
 Summary......Page 367
 Review Exercises......Page 369
 Chapter 7 Test......Page 370
8: Areas of Polygons and Circles......Page 371
 8.1 Area and Initial Postulates......Page 372
 8.2 Perimeter and Area of Polygons......Page 383
 8.3 Regular Polygons and Area......Page 393
 8.4 Circumference and Area of a Circle......Page 399
 8.5 More Area Relationships in the Circle......Page 407
 PERSPECTIVE ON APPLICATION: Another Look at the......Page 414
 Summary......Page 416
 Review Exercises......Page 418
 Chapter 8 Test......Page 420
9: Surfaces and Solids......Page 423
 9.1 Prisms, Area, and Volume......Page 424
 9.2 Pyramids, Area, and Volume......Page 433
 9.3 Cylinders and Cones......Page 444
 9.4 Polyhedrons and Spheres......Page 453
 PERSPECTIVE ON HISTORY: Sketch of René Deseartes......Page 463
 Summary......Page 464
 Review Exercises......Page 466
 Chapter 9 Test......Page 467
10: Analytic Geometry......Page 469
 10.1 The Rectangular Coordinate System......Page 470
 10.2 Graphs of Linear Equations and Slope......Page 478
 10.3 Preparing to Do Analytic Proofs......Page 486
 10.4 Analytic Proofs......Page 495
 10.5 Equations of Lines......Page 500
 PERSPECTIVE ON HISTORY: The Banach-Tarski Paradox......Page 508
 PERSPECTIVE ON APPLICATION: The Point Of Division Formulas......Page 509
 Review Exercises......Page 510
 Chapter 10 Test......Page 512
11: Introduction to Trigonometry......Page 515
 11.1 The Sine Ratio and Applications......Page 516
 11.2 The Cosine Ratio and Applications......Page 524
 11.3 The Tangent Ratio and Other Ratios......Page 531
 11.4 Applications with Acute Triangles......Page 540
 PERSPECTIVE ON HISTORY: Sketch of Plato......Page 549
 PERSPECTIVE ON APPLICATION: Radian Measure of Angles......Page 550
 Review Exercises......Page 552
 Chapter 11 Test......Page 554
 Appendix A: Algebra Review......Page 557
 Appendix B: Summary of Constructions, Postulates, and Theorems and Corollaries......Page 583
Answers......Page 591
 Selected Exercises and Proofs......Page 11
Glossary......Page 615
Index......Page 619