Learning Geometry Through Problem Solving

This new volume focuses on problem-solving in plane geometry topics and is suitable for any reader with elementary geometrical knowledge at the secondary school level. The author has assembled an exceptional collection of geometry exercises with approximately equal weight allocated among different types of problems: proofs, calculations, and geometric straightedge-and-compass constructions.

The book is divided into seven chapters, with sets of problems arranged in approximate order of increasing difficulty. The first chapter is devoted to a discussion of several useful strategies and techniques for approaching geometric problems. The next chapter presents warm-up exercises to "stretch" geometric muscles and refresh the very basic facts about topics covered in subsequent chapters. Each of the following chapters: "Triangles," "Quadrilaterals," "Circles," and "Areas" has three sections (A, B, and C), starting with simple problems and questions (section A), progressing to intermediate problems (section B), and ending with more advanced and complex challenges (section C), some of which were offered in math Olympiads and various math contests. The final chapter is a mixture of challenging problems comprising material covered in previous chapters.

At the end of the book, the "Solutions and Answers" section provides detailed explanations and solutions for all the problems. In that section, for many interesting problems, the author reveals not just one but multiple alternative solutions, compares them, and discusses their effectiveness. The emphasis is on how to acquire insight and develop different strategies for tackling geometrical challenges. By solving these problems, readers discover fascinating links between them, unlock geometrical secrets, build self-confidence, and - for many skeptics - discover that learning geometry can be fun and enjoyable!