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_{2}  S_{4} = S/2.
Geometry problem solving
Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an illstructured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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