Designed for high school students and teachers with an interest in mathematical problem-solving, this volume offers a wealth of nonroutine problems in geometry that stimulate students to explore unfamiliar or little-known aspects of mathematics. Included are nearly 200 problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and many other subjects. Within each topic, the problems are arranged in approximate order of difficulty. Detailed solutions (as well as hints) are provided for all problems, and specific answers for most. Invaluable as a supplement to a basic geometry textbook, this volume offers both further explorations on specific topics and practice in developing problem-solving techniques.

Table of Contents

SECTION I

A New Twist on Familiar Topics

1. Congruence and Parallelism

2. Triangles in Proportion

3. The Pythagorean Theorem

4. Circles Revisited

5. Area Relationships

SECTION II

Further Investigations

6. A Geometric Potpourri

7. Ptolemy and the Cyclic Quadrilateral

8. Menelaus and Ceva: Collinearity and Concurrency

9. The Simson Line

10. The Theorem of Stewart

Hints

Appendix I: Selected Definitions. Postulates. and Theorems

Appendix II: Selected Formulas