The figure
below shows a parallelogram ABCD of area
S with an exterior point E. If S_{1}, S_{2}, S_{3},
and S_{4}, are the areas of triangles EAB, EBC, ECD, and
EAD, respectively, prove that S_{1} + S_{3} = S_{4}
- S_{2} = S/2.

See also

Poster of Problem 1381