Plain Plane Geometry

Main subject categories: • Elementary Geometry • Plane Euclidean GeometryThe 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. 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. Request Inspection Copy "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"--Publisher Title 3 Copyright 4 Preface 7 1. Geometric figures 17 1.1 Points, lines, rays, line segments and length 17 1.2 Angles and the degree measure 21 1.3 The Parallel Postulate 27 1.4 The Corresponding Angles Axiom 30 1.5 Polygons 32 1.6 Circles 41 2. Congruent triangles 44 2.1 SAS Congruency Rule 45 2.2 SSS Congruency Rule 50 2.3 ASA and AAS Congruency Rules 58 2.4 SSA and RHS Congruency Rules 61 2.5 Angle bisectors in a triangle are concurrent 64 3. Quadrilaterals 67 3.1 Characterizations of a parallelogram 68 3.2 Areas 75 3.3 Pythagoras’s Theorem 85 4. Similar triangles 95 4.1 Basic Proportionality Theorem 97 4.2 Criteria for similarity of triangles 100 4.3 Areas of similar triangles 114 5. Circles 119 5.1 Area and circumference of a circle 123 5.2 Circular arcs 128 5.3 Tangent line to a circle 159 5.4 An excursion in inversion 167 Epilogue 179 Hints 182 Solutions 195 Bibliography 282 Index 284 Geometric figures Points, lines, rays, line segments and length Angles and the degree measure The parallel postulate The corresponding angles axiom Polygons Circles Congruent triangles SAS congruency rule SSS congruency rule ASA and AAS congruency rules SSA and RHSs congruency rules Angle bisectors in a triangle are concurrent Quadrilaterals Characterizations of a parallelogram Areas Pythagoras' theorem Similar triangles Basic proportionality theorem Criteria for similarity of triangles Areas of similar triangles Circles Area and circumference of a circle Circular arcs Tangent line to a circle An excursion in inversion Epilogue Hints Solutions.