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.
Geometry problem solving is one of the
most challenging skills for students to learn. When a problem
requires auxiliary construction, the difficulty of the problem
increases drastically, perhaps because deciding which
construction to make is an ill-structured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."