The segment joining the midpoints of the $2$ bases of a trapezoid passes through the intersection of its $2$ diagonals Prove that the segment line joining the midpoints of the $2$ bases of a trapezoid always passes through the intersection of the $2$ diagonals of the same trapezoid. 
I've tried to use Intercept theorem but it didn't work.

Hint: $\triangle AFC$ is similar to $ \triangle DFE$, next you can show that $\triangle AFG$ is similar to $ \triangle HFE$ and $ \angle AFG$ congruent to $\angle HFE$.
