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complete the proof for why the converse of the pythagorean theorem is false.
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suppose we let a, b, and c represent the sides of a triangle such that c is the longest side and a² + b² = c². this is the pythagorean theorem. if we assume the converse, namely that a² + b² = c² implies c is the longest side, then there is a possibility of a triangle where a > c or b > c. this contradicts the original assumption that c is the longest side of the triangle, therefore proving that the converse of the pythagorean theorem is false.
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