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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. The picture

I've tried to use Intercept theorem but it didn't work .

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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 $\angle HFE$.

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