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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 ABCDEF (namely AB and DE,BC and EF, and CD and FA) are parallel and equal in length.

 

(b) Show that triangles ACE and BDF have equal areas.

 

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

 Jul 3, 2020
edited by aDumbDude  Jul 3, 2020
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You should post the asymptote code with the problem!  That keeps it simple.

 Jul 3, 2020

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