Problem 356. Square, Point inside, Triangles, Area
Level: High School, College, SAT Prep.

The figure shows a square ABCD of area
S. A point P is inside the square. 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.