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) .
Geometry problem solving
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."