Problem 557: Quadrilateral, Midpoints, Sides, Varignon
Parallelogram, Area.
Level: High School, College, Math Education
The figure shows a quadrilateral ABCD. If E, F, G, and H are the
midpoints of the sides, prove that: (1) EFGH is a parallelogram known as Varignon
parallelogram; (2) Area of EFGH is one half the area ABCD.
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 illstructured 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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