Classical Geometry Euclidean Transformational Inversive and Projective 1st edition by Leonard, Lewis, Liu ISBN 1118679199 9781118679197

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Product details:

ISBN 10: 1118679199
ISBN 13:  9781118679197
Author: Leonard, Lewis, Liu

Written by well-known mathematical problem solvers, this book features up-to-date and applicable coverage of the wide spectrum of modern geometry and aids readers in learning the art of logical reasoning, modeling, and proof.

Classical Geometry Euclidean Transformational Inversive and Projective 1st Table of contents:

PART I: EUCLIDEAN GEOMETRY

• CHAPTER 1: CONGRUENCY

  • 1.1 Introduction

    • Assumed Knowledge

    • Notation and Terminology

  • 1.2 Congruent Figures

    • Theorem 1.2.1

    • The Basic Congruency Conditions

    • Axiom 1.2.2 (SAS Congruency)

    • Theorem 1.2.3 (SSS Congruency)

    • Theorem 1.2.4 (ASA Congruency)

    • Axiom 1.2.5 (The Triangle Inequality)

    • Theorem 1.2.6 (The Isosceles Triangle Theorem)

    • Theorem 1.2.7 (Converse of the Isosceles Triangle Theorem)

    • Exercise 1.2.8

    • Theorem 1.2.9 (The Angle-Side Inequality)

    • Theorem 1.2.10

  • 1.3 Parallel Lines

    • Theorem 1.3.1

    • Theorem 1.3.2

    • 1.3.1 Angles in a Triangle

      • Theorem 1.3.3

      • Theorem 1.3.4 (The Exterior Angle Theorem)

      • Corollary 1.3.5 (The Exterior Angle Inequality)

    • 1.3.2 Thales’ Theorem

      • Theorem 1.3.6 (Thales’ Theorem)

      • Corollary 1.3.7

      • Theorem 1.3.8 (Converse of Thales’ Theorem)

      • Exercise 1.3.9

    • 1.3.3 Quadrilaterals

      • Theorem 1.3.10

      • Theorem 1.3.11

      • Theorem 1.3.12

      • Example 1.3.13

      • Exercise 1.3.14

      • Example 1.3.15 (Simson’s Theorem)

  • 1.4 More About Congruency

    • Theorem 1.4.1 (SAA Congruency)

    • Theorem 1.4.2 (SSA+ Congruency)

    • Corollary 1.4.3 (HSR Congruency)

    • Counterexamples and Proof by Contradiction

    • Exercise 1.4.4

  • 1.5 Perpendiculars and Angle Bisectors

    • Theorem 1.5.1

    • Exercise 1.5.2

    • Exercise 1.5.3

    • Exercise 1.5.4

    • Exercise 1.5.5

    • Theorem 1.5.6 (Characterization of the Angle Bisector)

    • Inequalities in Proofs

    • Theorem 1.5.7 (Open Jaw Inequality)

  • 1.6 Construction Problems

    • Straightedge Operations

    • Compass Operations

    • Useful Facts in Justifying Constructions

    • Theorem 1.6.1

    • Basic Constructions

    • Exercise 1.6.2

    • Exercise 1.6.3

    • Exercise 1.6.4

    • Example 1.6.5

    • Example 1.6.6

    • Example 1.6.7

    • Example 1.6.8

    • Exercise 1.6.9

  • 1.6.1 The Method of Loci

    • Example 1.6.10

  • 1.7 Solutions to Selected Exercises

    • Solution to Exercise 1.2.8

    • Solution to Exercise 1.3.9

    • Solution to Exercise 1.3.14

    • Solution to Exercise 1.4.4

    • Solution to Exercise 1.5.2

    • Solution to Exercise 1.5.3

    • Solution to Exercise 1.5.4

  • 1.8 Problems

• CHAPTER 2: CONCURRENCY

  • 2.1 Perpendicular Bisectors

    • Theorem 2.1.1

    • Corollary 2.1.2

    • Theorem 2.1.3

    • Exercise 2.1.4

  • 2.2 Angle Bisectors

    • Theorem 2.2.1

    • Theorem 2.2.2

    • Proposition 2.2.3

    • Theorem 2.2.4

  • 2.3 Altitudes

    • Theorem 2.3.1

    • Exercise 2.3.2

    • Theorem 2.3.3

    • Exercise 2.3.4

    • Theorem 2.3.5

    • Theorem 2.3.6

    • Exercise 2.3.7

  • 2.4 Medians

    • Exercise 2.4.1

    • Theorem 2.4.2 (The Midline Theorem)

    • Lemma 2.4.3

    • Theorem 2.4.4

    • Theorem 2.4.5

  • 2.5 Construction Problems

    • Example 2.5.1

    • Example 2.5.2

    • Example 2.5.3

    • Thales’ Locus

    • Theorem 2.5.4

    • Example 2.5.5

    • Example 2.5.6

  • 2.6 Solutions to the Exercises

    • Solution to Exercise 2.1.4

    • Solution to Exercise 2.3.2

    • Solution to Exercise 2.3.4

    • Solution to Exercise 2.3.7

    • Solution to Exercise 2.4.1

  • 2.7 Problems

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Tags: Leonard, Lewis, Liu, Classical Geometry, Transformational Inversive