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The figure shows the squares ABCD and EFGH. S_{1}, S_{2}, S_{3}, and S_{4}, are the areas of the shaded quadrilaterals.Prove that: (1) AE^{2} + CG^{2} = BF^{2} + DH^{2}; (2) S_{1} + S_{3} = S_{2} + S_{4}. See also: Puzzle of problem 1182.

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