Problem 357. Square, Exterior point, Triangles, Area
Level: High School, College, SAT Prep. The figure shows a square ABCD of area S with an exterior point P. If S_{1}, S_{2}, S_{3}, and S_{4}, are the areas of triangles PAB, PBC, PCD, and PAD, respectively, prove that S_{1} + S_{3} = S_{4}  S_{2} = S/2.

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