The figure below shows a triangle
ABC with the median BM. AMDE and BMFG are squares so that MF meets
BC at H and DF meets AC and BC at Q and P, respectively. If S_{1},
S_{2}, S_{3}, and S_{4} are the areas of
triangles BHM, FHP, CPQ, and DMQ, respectively, prove that S_{1} +
S_{3} = S_{2} + S_{4}.
