Plain Plane Geometry

by Amol Sasane

Overview

The book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads.Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of 'play' in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.

Product Details

ISBN-13:	9789814740449
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	02/19/2016
Pages:	288
Product dimensions:	6.00(w) x 8.90(h) x 0.50(d)

Table of Contents

Preface vii

1 Geometric figures 1

1.1 Points, lines, rays, line segments and length 1

1.2 Angles and the degree measure 5

1.3 The Parallel Postulate 11

1.4 The Corresponding Angles Axiom 14

1.5 Polygons 16

1.6 Circles 25

2 Congruent triangles 29

2.1 SAS Congruency Rule 30

2.2 SSS Congruency Rule 35

2.3 ASA and AAS Congruency Rules 44

2.4 SSA and RHS Congruency Rules 48

2.5 Angle bisectors in a triangle are concurrent 51

3 Quadrilaterals 53

3.1 Characterizations of a parallelogram 54

3.2 Areas 61

3.3 Pythagoras's Theorem 72

4 Similar triangles 81

4.1 Basic Proportionality Theorem 83

4.2 Criteria for similarity of triangles 86

4.3 Areas of similar triangles 100

5 Circles 105

5.1 Area and circumference of a circle 109

5.2 Circular arcs 114

5.3 Tangent line to a circle 145

5.4 An excursion in inversion 153

Epilogue 163

Hints 167

Solutions 181

Bibliography 265

Index 267