what is a proof of the pythagoarean theorem?

Answer 1

http://www.mathsisfun.com/pythagoras.html

Answer 2

Imagine having 3 perfectly square boxes. Perfectly square meaning the Length(L) and Width(W) of each indivudal box are the same but of different total areas. Arrange them so that one of the boxes represents the "A" dimension of a right angle triangle. Another Box representing the "B" dimension of a right triangle and the last box representing the "C" dimension (hypotneuse) of the configured triangle. Looking at the individual boxes areas (L x W), a clear pattern exists. Since these boxes are perfectly square (L = W) we can say A^2 + B^2 = C^2. Meaning the area of "box C" is equal to the area of "box A" plus the area of "box B"