Pythagorean Theorem, Proof 115 The proof below is by Nileon M. Dimalaluan, Jr. and was published in the online journal Chiaroscuro of a High IQ Society (March 2004.) The proof is based on the following diagram: D a B C E. b A B' D' Since triangles ABC and AED are similar T atc Triangles EBD, EBC are equal, each with the area of =ra. 2 If F denotes the area of shape F, then [AAED] = [AABC] + 2[AEBC] so that -r( at c ) = 2 . Frat - ab , or, r(c - a) = ab. Substituting r = a(c ta) 2 results in b = b which is the Pythagorean theorem, b a2 + 62 = 02