Question

In the given figure, $ABC$ is an isosceles triangle in which $AB=AC$. If $E$ and $F$ be the midpoints of $AC$ and $AB$ respectively, then BE is equal to _______.

• A. $CF$
• B. $AB$
• C. $CE$
• D. $BF$

Answer 1

The correct option is A $CF$

Since, $AB=AC$
$\Rightarrow$ $\frac{1}{2}$ $AB=$ $\frac{1}{2}$ $AC$
$\Rightarrow$ $BF=EC$
Also, $AB=AC$

$\Rightarrow$ $\angle$ $B=$ $\angle$ $C$
[Angles opposite to equal sides are equal]
In $△$ $BEC$ and $△$ $CFB$, we have
$EC=FB$ .....(proved above)
$\angle$ $B=$ $\angle$ $C$ ....(proved above)
$BC=BC$ .....(common)
$\therefore$ $△$ $BEC$ $\cong$ $△$ $CFB$ ......(By SAS)
$\Rightarrow$ $BE=CF$ .....(By CPCT)