Journey through Geometry

This book covers the main facts you need to know and remember during and after studying Geometry. They are presented in a logical progression for your ease of understanding and subsequent reference. The following topics are covered: - The laws of logic, postulates, definitions, and theorems for the properties of plane and solid geometrical figures - Coordinate geometry, vectors, and transformation geometry - A brief presentation of the most famous theorem in projective geometry - A comparison of the fundamental differences between Euclidean, Lobachevsky, and Riemann Geometry. This book explores important formulas required for solving most geometrical problems. Some of them may not be included in traditional textbooks. For instance, there are six different formulas to find the area of a triangle. Similarly, a very simple formula to compute the distance from a point to a given line or plane is provided. The content addresses the needs of Geometry students learning the subject for the first time as well as experienced practitioners who want to refresh their knowledge of the subject. Our rich experience in teaching this course Geometry at high schools as well as at universities offers students who use this book to be better equipped to take standardized tests, exams, and the SAT. It also prepares students for taking the higher level courses of mathematics.