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explain why the pythagorean theorem works.
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the pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (longest side). this can be explained mathematically by considering a right triangle in which the two shorter sides are represented by x and y and the longest side is represented by z. when the squares of these three sides are calculated and added together, the result is x2 + y2 = z2, which is the pythagorean theorem.
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