On site, proof #2 is invalid. It establishes that two hypotenuses of right triangles of values a and b forms a square of value c^2. It fails to prove that the sum of a^2 and b^2 equals c^2. Counterexample:
Squares formed from each triangle equal a^2, b^2, and c^2, and because they are congruent triangles, their hypotenuses form right angles on outside, sharing similar square with value c^2. However, a^2 + b^2 is arbitrary and does not equal c^2.
I haven't looked at the other proofs, but I think it likely others are invalid if this one is.
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