# 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 $\angle HFE$.