Question

In triangle ABC, D is midpoint of AB, E is midpoint of AC, and F is midpoint of BC.
Prove segment AF and segment DE bisect each other. (note: you may need other segments).

Answer 1

Any ideas how to set this up in the general case for any triangle.

Answer 2

This seems straightforward enough, for X point of intersection,

ADE similar ABC -> DX = XE = BC/2 -> AF bisects DE AND
by the same reasoning AX = XF so DE bisects AF.