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      By Antonio Gutierrez
Problem 558: Quadrilateral, Trisection, Sides, Wittenbauer Parallelogram, Area. Level: High School, College, Math Education

The figure shows a quadrilateral ABCD. Points E, E', F, F', G, G', H, and H' trisect the sides AB, BC, CD, and AD, respectively. Extension of lines EH', E'F, F'G, and G'H meet at K, L, M and N, respectively. Prove that: (1) KLMN is a parallelogram known as Wittenbauer parallelogram; (2) Area of KLMN is 8/9 of area ABCD.

Wittenbauer Parallelogram, Trisection, Area


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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Geometry problems 541-550