If anyone needs help on this problem, this is what i did:

Construct a line from Q to the line CD that is parallel to the line AC. By Thm. 15, it intersects CD at its midpoint, P. You can then prove that triangles ACD and QPD are similar.

Do the same with midpoint E and create similar triangles in ABC and EBF. You can now use the midpoint theorem and ratios to prove that lines MN and PQ are equal.

BF 14 says if two lines are parallel (MN and AC) and there is another line parallel to it (PQ) then all the lines are parallel.

Hope this helps!

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Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva