Question

In fig, AD is the median and DE || AB. Prove that BE is a median of $\Delta ABC$.

Answer 1

In order to prove that BE is the median, it is sufficient to show that E is the mid-point of AC.
Now, AD is the median in $\Delta ABC$
$\Rightarrow$ D is the mid-point of BC.


Since, DE is a line drawn through the mid-point of side BC of $\Delta ABC$ and is parallel to AB (given). Therefore, E is the mid-point of AC (by converse of M.P.T) Hence, BE is the median of $\Delta ABC$.