Euclidean Plane Geometry

The content of the book is introduced in such a way that it does not depend on any previous knowledge of geometry. The first two chapters are devoted to the history and axiomatic foundations of geometry. The following two chapters are devoted to: the relation of congruence of figures, the use of congruence theorems for triangles and circles. In the fifth chapter, vectors are defined. Thales's theorem of proportion is proved. The sixth chapter is devoted to isometries and their use. The...
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The content of the book is introduced in such a way that it does not depend on any previous knowledge of geometry. The first two chapters are devoted to the history and axiomatic foundations of geometry. The following two chapters are devoted to: the relation of congruence of figures, the use of congruence theorems for triangles and circles. In the fifth chapter, vectors are defined. Thales's theorem of proportion is proved. The sixth chapter is devoted to isometries and their use. The classification of isometries is carried out. The seventh and eighth chapters are devoted to: similarity transformations, the relation of similarity and the area of a figures. The ninth chapter presents the inversion. At the end of each chapter (except the introductory one) are the exercises. Solutions and instructions can be found in the last, tenth chapter. The book contains 341 statements, 247 exercises and 418 solved problems (including 28 problems from the IMO). This means that the book is at the same time a guide for preparing for the IMO. For some well-known theorems and problems a brief historical remarks are given which might help high school and college students to better understand the development of geometry through the centuries.
This is a black and white version of the same book.