Machu Picchu, Geometry Problems, Online Education
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 865: Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity


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 | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 861-870 | Triangles | Parallelogram | Similarity, Proportions | Midpoint | Parallel | Email | Solution / comment | By Antonio Gutierrez