proof of Pythagorean theorem

This is a geometrical proof of Pythagorean theoremPlanetmathPlanetmathPlanetmath. We begin with our triangle:


Now we use the hypotenuseMathworldPlanetmath as one side of a square:


and draw in four more identical triangles


Now for the proof. We have a large square, with each side of length a+b, which is subdivided into one smaller square and four triangles. The area of the large square must be equal to the combined area of the shapes it is made out of, so we have

(a+b)2 = c2+4(12ab)
a2+b2+2ab = c2+2ab
a2+b2 = c2 (1)
Title proof of Pythagorean theorem
Canonical name ProofOfPythagoreanTheorem
Date of creation 2013-03-22 11:56:36
Last modified on 2013-03-22 11:56:36
Owner drini (3)
Last modified by drini (3)
Numerical id 8
Author drini (3)
Entry type Proof
Classification msc 51-00
Related topic PythagorasTheorem