Question
In $\triangle ABC, AD$ is the median and $DE,$ drawn parallel to side $BA,$ meets $AC$ at point $E.$
Show that $BE$ is also a median.
Show that $BE$ is also a median.
✓
Answer
In $\triangle ABC$
$AD$ is the median of $BC$.
$\Rightarrow D$ is the mid$-$point of $BC$.
Given at $DE \| BA$
By the Converse of the Mid-point theorem,
$\Rightarrow D$E bisects $AC$
$\Rightarrow E$ is the mid$-$point of $AC$
$\Rightarrow BE$ is the median of $AC$
that is $BE$ is also a median.
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