1. The proof which we present for the Pythagorean theorem has the advantage that it uses the previous theorem, Theorem 3.3 in conjunction with many of the results which were obtained in section 1. However, there is a direct way to obtain this result.
Theorem: (Pythagoras) If a, b, and c are the sides in a right triangle then
The proof uses a lemma
Lemma: If A = (x1, y1), B = (x2, y2) and C = (x3, y3) are the vertices of a right triangle then