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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.

Varignon Parallelogram Area, Midpoint

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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