Online Geometry
Problem 473. Triangle, Parallel, Side, Parallelogram,
Area, Similarity

The figure shows a triangle ABC of
area S. Lines DE, FG, and HM are parallel to AC, BC, and AB
respectively. If S_{1}, S_{2}, S_{3},
and S_{4} are the areas of triangles DFN, PME, HGQ, and
NPQ respectively, prove that
.