Question

State true or false:

In $△ABC$, $AD$ is the median and $DE$ is parallel to $BA$, where $E$ is a point in $AC$ and hence $BE$ is parallel to $BC$.

• A. True
• B. False

Answer 1

The correct option is B False

Given: $AD$ is the median of $△ABC$.
Hence, $BD=DC$.
Also, $DE\parallel AB$ and $DE$ is drawn from the mid point of $BC$, i.e. $D$.

Thus, by converse of mid-point theorem, $DE$ bisects the third side, which is $AC$.
Then, $E$ is the mid point of $AC$.

Hence, $BE$ is the median of $△ABC$.

That is, the given statement is false and option $B$ is correct.