Question

$△ABC$ is iscoeles in which $AB=AC$, seg $BD$ and seg $CE$ are medians show that $BD=CE$.

Answer 1

In $△ABC,AB=AC$ $\Rightarrow \frac{1}{2}AB=\frac{1}{2}AC....\left(1\right)$

$\angle B=\angle C......\left(2\right)$

In$△BEC$ & $△CDB$
$\angle EBC=\angle DCB$(From 2)
$EB=DC$ (From E to D are mid points of AB & AC)

$BC=CB$ (Common)
$\angle BEC\cong \angle CDB$ (By SAS)

$EC=DB$ (By C.P.C.T)