In the figure below, ABCD is a
quadrilateral with E, F, G, and H, midpoints of AB, BC, CD, and
AD respectively. Lines AF, BG, CH and DE determine the shaded
regions of areas S, S_{1}, S_{2}, S_{3}, and S_{4}. Prove that S = S_{1} + S_{2} + S_{3} + S_{4}.
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by Antonio Gutierrez
