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Online Geometry Problem 864: Parallelogram, Diagonal, Congruence, Similarity, Metric Relations. Level: High School, College, Mathematics Education

The figure below shows a parallelogram ABCD. E is a point on AD extended. BE cuts AC at F and CD at G. If BF = EG and BC = 3, find AE.


Geometry problem 864: Parallelogram, Congruence, Similarity, Metric Relations


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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