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.