Let \(ABCDEF\) be a convex hexagon. Let \(A', B', C', D', E', F' \) be the centroids of triangles \(FAB, ABC, BCD, CDE, DEF, EFA\), respectively.

(a) Show that every pair of opposite sides in hexagon \(A'B'C'D'E'F'\) (namely \(A'B'\) and \(D'E', B'C'\) and \(E'F',\) and \(C'D'\) and \(F'A'\)) are parallel and equal in length.

(b) Show that triangles \(A'C'E'\) and \(B'D'F'\) have equal areas.

And also, how do I insert an asymptote diagram in my question? Thanks!

aDumbDude Jul 3, 2020