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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." 

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