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The proof I made was this:

Make 4 congruent right triangles with side lengths of "a" and "b" and a hypotenuse with a length "c" and put the triangles together to make a square where the hypotenuses of the triangles are on the outside of the square. it should look like this: http://4.bp.blogspot.com/-YF-2E8vTRLs/TmoSmBD65wI/AAAAAAAABX8/BPFkCMM0vGE/s1600/QST.png

Obviously the area of the triangle is A=c^2, the Area could also be the area of each triangle A=1/2ab, there are 4 of them so it becomes A=2ab. Through substitution we get c^2=2ab.

c^2=2ab doesn't agree with the Pythagorean theorem, the problem I have having is explaining why this is so... I cant find an error in my logic. So can you guys help me out and tell me where I went wrong?