###### Online Geometry Problem 865: Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity. Level: High School, College, Mathematics 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.       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."
 Home | Search | Geometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 861-870 | Triangles | Parallelogram | Similarity, Proportions | Midpoint | Parallel | Email | Solution / comment | By Antonio Gutierrez