Question

In trangle ABC, AD is the median and DE, drawn parallel to side BA, meets AC at point E, show that BE is also a median.

Answer 1

reffer image

in $△ABC$ and $\triangle DEC$

$BC||DC$

$BA||DE$.......(given)

$AC||EC$ then

then $\Delta ABC\sim \Delta DEC$

then ,$\frac{AC}{BC}=\frac{EC}{DC}$

$BC=2Dc$

then $AC=2EC$

$E$ is midpoint of $AC$.

$BE$ is also a median.