In the figure below, ABCD is a parallelogram with E an exterior point. F and G are the points of intersection of AE with BD and BC. H is the point of intersection of DE and BC. If S, S1, S2, and S3 are the areas of quadrilateral DFGH, and triangles ABF, BEG, and CEH respectively, prove that S = S1 + S2 + S3 . Post a comment or solution.