ABSTRACT
Pythagorean theorem concerns the relationship of the sides of a right triangle that can be extended to the study of all types of triangles, relationships concerning circles, key trigonometric relationships, and concepts of area. The Law of Sines and the Law of Cosines derive all the congruence theorems that are taught in geometry. Applications of similarity range from the mundane to the surprising. Similarity is also used in radiation therapy for cancer patients for accuracy in focusing the beam. Recall that the Law of Cosines essentially depended on the Pythagorean Theorem which, in turn, depended on the concept of area. Other than congruence and similarity, the main theorems in a geometry course are those concerning circles, their chords, their tangents, and their secants. The proof of Ptolemy's Theorem uses similar triangles. A cevian in a triangle is a line drawn from a vertex to the opposite side of a triangle.
