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
S_{1}, S_{2}, S_{3}, and S_{4} are the blue shaded areas, prove that S = S_{1} +
S_{2} + S_{3} + S_{4}
