Thread: triangle

In triangle ABC , the midpoint of BC is D . THe line that passes through B and parallel to DA intersects CA produced at E . THe line that passes through C and parallel to DA intersects BA produced at F . Prove that BE=CF .

a is the midpoint of CE and BF

from this and with parallel lines
it is easy to prove that triangles EBA and ACF are the same
and therefor BE = CF

can you build on this....