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AD and BE are medians BE || DF
Prove : CF = 1 4 AC
AE = CE
BD = DC
DF = OE

Dear Student,
Here is the solution of your asked query:

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

Regards

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In triangle EBC, since D is the midpoint of BC and DF II BE,by using the converse of the midpoint theorem, weget that CF = FE, i.e, F is the midpoint of of CE.

Now, since E is the midpoint of AC, AE= CE.

AC + CE = AC

= AE + 2CF = AC ( AF = CF)

= 2CF + 2CF = AC ( AE = CE)

4CF = AC

Therefore, CF = 1/4 AC

Hence, proved.
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