Let points D, E, and F lie on the sidelines
BC, CA, and AB respectively of ΔABC.

The lines AD, BE, and CF are nonparallel and
concurrent at a point not on any of the sidelines.

Prove that the triangles BDF and CED have the
same orientation and equal areas if and only if
D is the midpoint of side BC.

(In reply to Possible solution by broll)

Triangles BDF and CED have the same orientation if when reading the vertices you read them clockwise or counter clockwise.

Posted by Bractals on 2012-02-19 14:07:11