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