Problem 402. Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity. Level: High School, College, SAT Prep.

The figure shows a hexagon ABCDEF. G, H, J, K, L, and M are the centroids of triangles ABC, BCD, CDE, DEF, EFA, and FAB, respectively. Prove that the hexagon GHJKLM has opposite sides parallel and of equal length.
The centroid of a triangle is the point of intersection of its medians.