True or false: If  $AD$ and $CE$are medians in the given figure, and  $DF\parallel CE$then $FB=\frac{1}{4}AB$

 

Concept: Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Given: D and  E are mid points of BC and AB ,Respectively(since) AD  and  CE (ARE MEDIANS ) AND 

$DF\parallel CE$ In  $\Delta BEC,$ $FD\parallel CE$    and  D is mid point of BC.

Then, by converse of mid point theorem, F is mid point of BE.

That is,  

$$\begin{gathered} FB=\frac{1}{2}\left(BE\right) \\ FB=\frac{1}{2}\left(\frac{1}{2}AB\right)......(E is mid point of AB, i.e. ) \end{gathered}$$

$FB=\frac{1}{4}AB$

Hence, the given statement is true and option 1 is correct.