Question

In the adjoining figure, $AD$ is a median of $△ABC$ and $DE\parallel BA$. Show that $BE$ is also a median of $△ABC$.

Answer 1

Consider $△ABC$

It is given that $DE\parallel AB$

We know that $D$ is the midpoint of $BC$

Based on the midpoint theorem we know that $E$ is also the midpoint of $AC$

$\therefore$ $BE$ is the median of $△ABC$ drawn through $B$

Hence, it is proved that $BE$ is also a median of $△ABC$.