The figure below shows a triangle ABC with M
midpoint of AC. AD, BM, and CF meet at E. S, S_{1}, S_{2},
S_{3}, S_{4}, S_{5}, and S_{6}, are the areas of
triangles ABC, EAF, EFB, EBD, EDC, ECM, and EMA, respectively_{ }
.
Prove
that S_{1} + S_{3} + S_{5} = S_{2} + S_{4}
+ S_{6} = S/2.
