The figure below shows a
triangle ABC and the parallelograms ABDE and BCFG. ED and FG
extended meet at H. AJ and CK are parallel to BG (J on DE, K on
FG). JK cuts AB and
BC at L and M, respectively. If S is the yellow shaded area, and
S1, S2, S3, and S4 are the blue shaded areas, prove that S = S1 +
S2 + S3 + S4
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