Online Geometry Problem 865: Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity. Level: High School, College, Math Education

The figure below shows a parallelogram ABCD
with E midpoint of BC, O midpoint of BD and F midpoint of AD. G is a
point on CD. GE and DB extended meet at H. If OM is parallel to AD (M on
HF), prove that ME is parallel to FG.