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Edition: 08

Copyright: 2008

Publisher: Jones & Bartlett Publishers

Published: 2008

International: No

Copyright: 2008

Publisher: Jones & Bartlett Publishers

Published: 2008

International: No

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Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on how to solve challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next, through numerous problem solving techniques. A large collection of problems, varying in level of difficulty, are integrated throughout the text, and suggested hints for the more challenging problems appear in the instructor's solutions manual for use at instructor's discretion.

**0. Prologue**

1. The Treasure Island Problem

2. The Nine-Point Circle

3. Morley's Theorem

4. The Hiker's Path

5. The Shortest Highway

6. Steiner's Minimum Distance Problem

7. The Pythagorean Theorem

**1. Congruence, Constructions, and the Parallel Postulate**

1-1 Angles and Their Measurement

1-2 Congruences of Triangles

1-3 The Parallel Postulate and Its Consequences

1-4 More on Construction

**2. Circles**

2-1 Basic Properties of Arcs, Central and Inscribed Angles

2-2 Circles Inscribed in Polygons

2-3 More on Constructions

**3. Area and the Pythagorean Theorem**

3-1 Areas of Polygons

3-2 The Pythagorean Theorem

3-3 The Distance Formula

**4. Similarity**

4-1 Ratio, Proportion and Similar Polygons

4-2 Further Applications of the Side Splitting Theorem and Similarity

4-3 Areas of Similar Figures

4-4 The Golden Ratio and the Construction of a Regular Pentagon

4-5 Circumference and Area of a Circle

4-6 Other Recursive Formulas for Evaluating p

4-7 Trigonometric Functions

**5. Isometries**

5-1 Reflections, Translations, and Rotations

5-2 Congruence and Euclidean Constructions

5-3 More on Extremal Problems

5-4 Similarity Transformation with Applications to Constructions

**6. Composition of Transformations and Transformation Groups**

6-1 In Search for New Isometries

6-2 Composition of Rotations, The Treasure Island Problems and Other Treasures

**7. More Recent Discoveries**

7-1 The Nine-Point Circle and Other Results

7-2 Complex Numbers and Geometry

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Summary

Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on how to solve challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next, through numerous problem solving techniques. A large collection of problems, varying in level of difficulty, are integrated throughout the text, and suggested hints for the more challenging problems appear in the instructor's solutions manual for use at instructor's discretion.

Table of Contents

**0. Prologue**

1. The Treasure Island Problem

2. The Nine-Point Circle

3. Morley's Theorem

4. The Hiker's Path

5. The Shortest Highway

6. Steiner's Minimum Distance Problem

7. The Pythagorean Theorem

**1. Congruence, Constructions, and the Parallel Postulate**

1-1 Angles and Their Measurement

1-2 Congruences of Triangles

1-3 The Parallel Postulate and Its Consequences

1-4 More on Construction

**2. Circles**

2-1 Basic Properties of Arcs, Central and Inscribed Angles

2-2 Circles Inscribed in Polygons

2-3 More on Constructions

**3. Area and the Pythagorean Theorem**

3-1 Areas of Polygons

3-2 The Pythagorean Theorem

3-3 The Distance Formula

**4. Similarity**

4-1 Ratio, Proportion and Similar Polygons

4-2 Further Applications of the Side Splitting Theorem and Similarity

4-3 Areas of Similar Figures

4-4 The Golden Ratio and the Construction of a Regular Pentagon

4-5 Circumference and Area of a Circle

4-6 Other Recursive Formulas for Evaluating p

4-7 Trigonometric Functions

**5. Isometries**

5-1 Reflections, Translations, and Rotations

5-2 Congruence and Euclidean Constructions

5-3 More on Extremal Problems

5-4 Similarity Transformation with Applications to Constructions

**6. Composition of Transformations and Transformation Groups**

6-1 In Search for New Isometries

6-2 Composition of Rotations, The Treasure Island Problems and Other Treasures

**7. More Recent Discoveries**

7-1 The Nine-Point Circle and Other Results

7-2 Complex Numbers and Geometry

Publisher Info

Publisher: Jones & Bartlett Publishers

Published: 2008

International: No

Published: 2008

International: No

**0. Prologue**

1. The Treasure Island Problem

2. The Nine-Point Circle

3. Morley's Theorem

4. The Hiker's Path

5. The Shortest Highway

6. Steiner's Minimum Distance Problem

7. The Pythagorean Theorem

**1. Congruence, Constructions, and the Parallel Postulate**

1-1 Angles and Their Measurement

1-2 Congruences of Triangles

1-3 The Parallel Postulate and Its Consequences

1-4 More on Construction

**2. Circles**

2-1 Basic Properties of Arcs, Central and Inscribed Angles

2-2 Circles Inscribed in Polygons

2-3 More on Constructions

**3. Area and the Pythagorean Theorem**

3-1 Areas of Polygons

3-2 The Pythagorean Theorem

3-3 The Distance Formula

**4. Similarity**

4-1 Ratio, Proportion and Similar Polygons

4-2 Further Applications of the Side Splitting Theorem and Similarity

4-3 Areas of Similar Figures

4-4 The Golden Ratio and the Construction of a Regular Pentagon

4-5 Circumference and Area of a Circle

4-6 Other Recursive Formulas for Evaluating p

4-7 Trigonometric Functions

**5. Isometries**

5-1 Reflections, Translations, and Rotations

5-2 Congruence and Euclidean Constructions

5-3 More on Extremal Problems

5-4 Similarity Transformation with Applications to Constructions

**6. Composition of Transformations and Transformation Groups**

6-1 In Search for New Isometries

6-2 Composition of Rotations, The Treasure Island Problems and Other Treasures

**7. More Recent Discoveries**

7-1 The Nine-Point Circle and Other Results

7-2 Complex Numbers and Geometry