Euclidean and Transformational Geometry : Deductive Inquiry

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