Geometry. Ray Jurgensen, Alfred Donnelly, John Maier, Gerald Rising

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ПРОДАДЕНА

Автор:Ray Jurgensen, Alfred Donnelly, John Maier, Gerald Rising
Издателство:Houghtnon Mifflin Company
Страници:256
Корици:Твърди
Година:1978
Броя:1
ISBN:0-395-25669-0 Тегло (гр.): Формат: 195 / 245 Състояние: Мн. добро
Geometry - Ray Jurgensen, Alfred Donnelly, John Maier, Gerald Rising / Английски език
THE AUTHORS:
* Ray C. Jurgensen, Chairman of the Mathematics Department and holder of the Eppley Chair of Mathematics, Culver Academies, Culver, Indiana.
* Alfred J. Donnelly, Master Instructor and holder of the William Pitt Oakes Chair of Mathematics, Culver Academies.
* John E. Maier, formerly Master Instructor in Mathematics at Culver Academies.
* Gerald R. Rising, Professor and Chairman, Department of Instruction, State University of New York at Buffalo.

EDITORIAL ADVISER
Albert E. Meder, Jr., Dean and Vice Provost and Professor of Mathematics, Emeritus, Rutgers University, The State University of New Jersey.
The authors wish to express their appreciation to Miriam M. Schaefer for the work she did in preparing the optional computer sections for this text.
COPYRIGHT © 1978. 1975.by Houghton Mifflin Company
All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system, withaut permission in writing from the publisher. Printed in the United States of America.
ISBN: 0-395-25669-0

***
CONTENTS
Chapter 1 Elements of Geometry 1
Points, Lines, and Planes 1
1-1 Undefined Terms and Basic Definitions 1
1 -2 First Postulates and Theorems 5
Subsets of a Line 9
1-3 Segments and Rays 9
1-4 The Ruler Postulate 13
Careers in Geology 1 7
Proofs in Geometry 1 8
1 -5 Deductive Reasoning 1 8
1-6 If-Then Statements 22
1-7 Proofs in Two-Column Form 25
Chapter Summary 28
Chapter Test 29
Chapter Review 30
Reviewing Algebraic Skills 31
Programming in BASIC 32
Extra for Experts: Möbius Bands 35
Chapter 2 Angles; Perpendicular Lines 37
Angles and Their Measure 37
2-1 Angles and Half-Planes 37
2-2 The Protractor 41
2-3 Special Angles 45
Theorems 51
2-4 Forming Certain Angles 51
2-5 Right Angles and Perpendicular Lines 54
2-6 Complementary and Supplementary Angles 59
2-7 Demonstration of a Theorem 63
Chapter Summary 68
Chapter Test 69
Chapter Review 70
Reviewing Algebraic Skills 71
Programming in BASIC 72
Extra for Experts: Paradoxes 74
Chapter 3 Parallel Lines and Planes 7 7
When Lines and Planes Are Parallel 77
3-1 Definitions 77
3-2 When Lines Are Parallel 80
3-3 Indirect Proof 84
Careers in Construction 88
Proving that Lines Are Parallel 89
3-4 Converses of Theorems 89
3-5 A Parallel and a Perpendicular to a Line 92
Applying Parallel Lines to Polygons 96
3-6 The Angles of a Triangle " 96
3-7 The Angles of a Polygon 101
Chapter Summary 108
Chapter Test 108
Chapter Review 1 1 0
Programming in BASIC 1 1 1
Cumulative Review: Chapters 1-3 114
Chapter 4 Congruent Triangles 1 1 7
Proving That Triangles Are Congruent 1 1 7
4-1 Congruence of Triangles 117
4-2 Some Ways to Prove Triangles Congruent 121
4-3 Some Ways to Prove Right Triangles Congruent 125
Methods Involving Two Angles 131
4-4 More Ways to Prove Triangles Congruent 131
4-5 More Ways to Prove Right Triangles Congruent 135
Congruent Segments and Angles 139
4-6 Proving Corresponding Parts Congruent 1 39
4-7 Isosceles Triangles 143
Chapter Summary 148
Chapter Test 148
Chapter Review 150
Reviewing Algebraic Skills 152
Extra for Experts: The Hypotenuse-Leg Proposition 153
Chapter 5 Applying Congruent Triangles 155
Parallelograms 155
5-1 Properties of Parallelograms 155
5-2 Proving that Certain Quadrilaterals Are Parallelograms 158
Other Quadrilaterals 163
5-3 Rectangles, Rhombuses, Squares 163
5-4 Trapezoids 167
Inequalities 170
5-5 Inequalities for One Triangle170
5-6 The Triangle Inequality 176
5-7 Inequalities for Two Triangles 178
Chapter Summary 182
Chapter Test 183
Chapter Review 184
Extra for Experts: Mathematics and Magic 186
Careers in Medicine 187
Chapter 6 Similar Polygons 189
Definitions and Properties 189
6-1 Ratio and Proportion 189
6-2 Properties of Proportions 193
6-3 Similar Polygons 196
Careers in Graphic Arts 203
Working with Similar Triangles 204
6-4 Proving Triangles Similar 204
6-5 Segments Divided Proportionally 209
Chapter Summary 214
Chapter Test 215
Chapter Review 216
Programming in BASIC 218
Extra for Experts 220
Cumulative Review: Chapters 1-6 222
Chapter 7 Right Triangles 233
The Pythagorean Theorem 233
7-1 The Altitude to the Hypotenuse of a Right Triangle 233
7-2 The Pythagorean Theorem 237
7-3 Special Right Triangles 242
7-4 Rectangular Solids 246
Trigonometry 250
7-5 The Tangent Ratio 250
7-6 The Sine and Cosine Ratios 254
7-7 Using the Three Trigonometric Ratios 258
Table of Trigonometric Ratios 262
Chapter 10 Constructions and Loci 349
The Basic Constructions 349
10-1 Meaning of Construction 349
10-2 Parallel Lines and Perpendicular Lines 355
10-3 Constructions and Circles « 360
10-4 Special Segments 368
Careers in Architecture 373
Locus 374
10-5 Describing a Locus 374
10-6 Loci 378
10-7 Constructions and Loci - 381
Chapter Summary 385
Chapter Test 385
Chapter Review 387
Extra for Experts 388
Chapter 11 Coordinate Geometry 391
The Coordinate Plane 391
1 1-1 Location in the Plane 391
11-2 The Distance Formula 395
Segments and Lines 398
11-3 The Midpoint Formula 398
1 1-4 The Slope of a Line 400
1 1-5 Parallel and Perpendicular Lines 403
1 1 -6 The Equation of a Line 406
Careers in Navigation 41 1
Proofs Using Coordinate Geometry 412
11-7 Organizing Coordinate Proofs 412
1 1 -8 Proofs of Properties of Polygons 417
Chapter Summary 420
Chapter Test 421
Chapter Review 422
Programming in BASIC 424
Chapter 12 Transformations 427
Some Basic Mappings 427
12-1 Mappings and Congruence Mappings 427
12-2 Reflections 432
12-3 Half-Turns 437
Careers in Chemistry 442
Mappings and Compositions of Mappings 443
1 2-4 Self-Congruence and Symmetry 443
1 2-5 Composition of Mappings 447
12-6 Rotations 451
12-7 Translations 455
12-8 Dilations 460
Chapter Summary 463
Chapter Test 463
Chapter Review 465
Programming in BASIC 467
Extra for Experts: Glide Reflections 469
Cumulative Review: Chapters 7-12 471
Examination Questions 477
Trisecting an Angle 489
Postulates 493
Theorems 495
Answers to Self-Tests 502
Glossary 509
Index 519
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