# Geometry

## A High School Course

Textbook

1. Front Matter
Pages i-xxiii
2. Serge Lang, Gene Murrow
Pages 1-84
3. Serge Lang, Gene Murrow
Pages 85-106
4. Serge Lang, Gene Murrow
Pages 107-141
5. Serge Lang, Gene Murrow
Pages 142-160
6. Serge Lang, Gene Murrow
Pages 161-204
7. Serge Lang, Gene Murrow
Pages 205-222
8. Serge Lang, Gene Murrow
Pages 223-258
9. Serge Lang, Gene Murrow
Pages 259-323
10. Serge Lang, Gene Murrow
Pages 324-352
11. Serge Lang, Gene Murrow
Pages 353-386
12. Serge Lang, Gene Murrow
Pages 387-431
13. Serge Lang, Gene Murrow
Pages 432-466
14. Back Matter
Pages 467-470

### Introduction

A geometry course based on this book was taught success­ fully by Gene Murrow for several years. We are much indebted to Springer-Verlag for publishing Geometry, so that others can try our approach. The publishers and we thought it would be appropriate to issue the book first in a preliml. nary edition, on which we would welcome comments, especially from students and teachers of the high school geometry course. Such comments can bear on any aspect of Geometry, ranging from the choice of topics, the ordering of the topics, and other global considerations, to possible computational errors and misprints. We shall welcome criticisms and suggestions. Serge Lang Gene Murrow Contents Theorems Proved in Geometry xi xvii Introduction CHAPTER 1 -Distance and Angles 51. Lines 1 52. Distance 12 53. Angles 20 54. Proofs 43 55. Right Angles and Perpendicularity 52 86. The Angles of a Triangle 65 CHAPTER 2 - Coordinates 51. Coordinate Systems 85 52. Distance between Points on a Line 94 53. Equation of a Line 96 CHAPTER 3 - Area and the Pythagoras Theorem 51. The Area of a Triangle 107 S2. The Pythagoras Theorem 125 viii CONTENTS CHAPTER 4 - The Distance Formula Sl. Distance between Arbitrary Points 142 S2. Higher Dimensional Space 148 S3. Equation of a Circle 155 CHAPTER 5 - Some Applications of Right Triangles S1. Perpendicular Bisector 162 S2. Isosceles and Equilateral Triangles 175 S3. Theorems About Circles 190 CHAPTER 6 - Polygons S1.

### Keywords

Area Geometrie Geometry Pythagoras aspect boundary element method computation edition issue polygon proof publishing school theorem triangle

#### Authors and affiliations

1. 1.Department of MathematicsYale UniversityNew HavenUSA
2. 2.ArdsleyUSA

### Bibliographic information

• Book Title Geometry
• Book Subtitle A High School Course
• Authors S. Lang
G. Murrow
• DOI https://doi.org/10.1007/978-1-4757-1797-6
• Copyright Information Springer-Verlag New York 1983
• Publisher Name Springer, New York, NY
• eBook Packages
• Softcover ISBN 978-0-387-90727-7
• eBook ISBN 978-1-4757-1797-6
• Edition Number 1
• Number of Pages XXIII, 470
• Number of Illustrations 43 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site