AD and BE are medians of triangle ABC and DF parallel BE.Prove that CF =1fourth AC?

Let us observe the following figure.

Consider the triangle ABC.

AD and BE are the medians of the triangle.

Thus, D is the midpoint of the side BC and E is the midpoint of the side AC.

Therefore,

Consider the triangle BEC.

Given that DF is parallel to BE.

Therefore, F is the midpoint of CE.

That is

Thus, it has been proved that

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