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Let a, b, c be the sides of a triangle
and A, B, C the angles opposite those sides.
Then c2 = a2 + b2 - 2ab cos C.
Since ab is non-zero, this proves that
c2 = a2 + b2 iff cos C = 0, which
is equivalent to C being a right angle.
(In other words: the Pythagorean Theorem
and its converse.)