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.
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."