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question:

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', 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.

Image:

 

 

Hello, to solve question (a) you are only required to prove one pair of the hexagon are equal and parallel. I've chosen A'B' and E'D' for this. I've proved that they are parallel using segment FC, but I'm not sure how to prove that they are equal, nor am I able to do part (b). I'd appreciate some help in the correct direction. Thank you in advance :)

 
 Jul 22, 2021
 #1
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This is easy if you use coordinates.

 
 Jul 22, 2021
 #2
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I'm not sure what you mean by coordinates...

 
Guest Jul 22, 2021

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