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Problem 518: Parallelogram, Five Squares, Centers, 45 Degrees, Measure. Level: High School, College, SAT Prep.

The drawing shows a parallelogram ABCD with the squares of center E, F, G, and H. Prove that (1) EFGH is a square, (2) Formula to prove.
 

Parallelogram with five squares problem
 

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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