Question

In the adjoining figure, AD and BE are the medians of triangle ABC and DF is parallel to BE, Show that CF= 1/4 AC

Answer 1

BE is median therefore E is midpt of AC
AE=CE=1\2×AC.............(1)
Given that AD is median therefore D is midpt of BC
Also DF is parallel to BE(that is also third side of triangle BEC)
therefore by converse of the midpt theorem F is mid point of CE
hence CF = 1\2×CE

by eq. (1)
CF=1\2×CE
CF=1\2×1\2×AC
CF=1\4×AC

Answer 2

In this figure,E is the midpoint of AC  then AE =1/2 AC.

Now , DF // BE , then EF= 1/2 EC (Converse of midpoint theorem) .

Now , CF = 1/2 (1/2 AC)

               = 1/4 AC

              Hence Proved.