Pythagoras Proof

by paulgrimshaw - uploaded on April 2, 2017, 11:17 am

Proving Pythagoras theorem by splitting the triangle into two smaller triangles, X & Y. All triangles are similar, and therefore their areas are proportional to the squares of their hypotenuse, i.e.: area = k times hypotenuse^2 for a fixed k across all the triangles. As the hypotenuse of the triangles are a, b and c, and the area of the large triangle is the sum of the areas of the smaller triangles, we get k.c^2 = k.a^2 + k.b^2, so c^2 = a^2 + b^2.