Question

State true or false:

In the given figure, $AD$ and $CE$ are medians and $DF\parallel CE$, then $FB=\frac{1}{4}AB$.

• A. True
• B. False

Answer 1

The correct option is A True

Given: $D$ and $E$ are mid points of $BC$ and $AB$, respectively (since $AD$ and $CE$ are medians) and $DF\parallel CE$.

In $△BEC$,
$FD\parallel CE$ and $D$ is mid point of $BC$.
Then, by converse of mid point theorem, $F$ is mid point of $BE$.
That is, $FB=\frac{1}{2}\left(BE\right)$
$⟹$ $FB=\frac{1}{2}\left(\frac{1}{2}AB\right)$ ......($E$ is mid point of $AB$, i.e. $BE=\frac{1}{2}AB$)
$⟹$ $FB=\frac{1}{4}AB$.

Hence, the given statement is true and option $A$ is correct.