Elementary geometry for college students

✍ Scribed by Alexander, Daniel C.; Koeberlein, Geralyn M

Publisher: Brooks/Cole
Year: 2011
Tongue: English
Leaves: 628
Edition: 5th ed
Category: Library

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✦ Synopsis

Parallel lines -- the parallel postulate and special angles -- Indirect proof -- Proving lines parallel -- The angles of a triangle -- Convex polygons -- Symmetry and transformations -- Sketch of Euclid -- Non-Euclidean geometrics;3. Triangles -- Congruent triangles -- Corresponding parts of congruent triangles -- Isosceles triangles -- Basic constructions justified -- Inequalities in a triangle -- Sketch of Archimedes -- Pascal's triangle;6. Circles -- Circles and related segments and angles -- More angle measures in the circle -- Line and segment relationships in the circle -- Some constructions and inequalities for the circle -- Circumference of the earth -- Sum of the interior angles of a polygon;8. Areas of polygons and circles -- Area and initial postulates -- Perimeter and area of polygons -- Regular polygons and area -- Circumference and area of a circle -- More area relationships in the circle -- Sketch of Pythagoras -- Another look at the Pythagorean theorem;10. Analytic geometry -- The rectangular coordinate system -- Graphs of linear equations and slope -- Preparing to do analytic proofs -- Analytic proofs -- Equations of lines -- The Banach-Tarski paradox -- The point-of-division formulas;4. Quadrilaterals -- Properties of a parallelogram -- The parallelogram and kite -- The rectangle, square, and rhombus -- The trapezoid -- Sketch of Thales -- Square numbers as sums;5. Similar triangles -- Ratios, rates, proportions -- Similar polygons -- Proving triangles similar -- The Pythagorean theorem -- Special right triangles -- Segments divided proportionally -- Ceva's proof -- An unusual application of similar triangles;11. Introduction to trigonometry -- The sine ratio and applications -- The cosine ratio and applications -- The tangent ratio and other ratios -- Applications with acute triangles -- Sketch of Plato -- Radian measure of angles -- Appendix A: Algebra review -- Appendix B: Summary of constructions, postulates, theorems, and corollaries;1. Line and angle relationships -- Sets, statements, and reasoning -- Early definitions and postulates -- Angles and their relationships -- Introduction to geometric proof -- Relationships: perpendicular lines -- The formal proof of a theorem -- The development of geometry -- Patterns;7. Locus and concurrence -- Locus of points -- Concurrence of lines -- More about regular polygons -- The value of pi -- The nine-point circle;9. Surfaces and solids -- Prisms, area, and volume -- Pyramids, area, and volume -- Cylinders and cones -- Polyhedrons and spheres -- Sketch of René Descartes -- Birds in flight

✦ Table of Contents

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