Question

# State true or false:In $$\bigtriangleup ABC$$, $$AD$$ 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

Solution

## The correct option is B FalseGiven: $$AD$$ is the median of $$\triangle ABC$$.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 $$\triangle ABC$$.That is, the given statement is false and option $$B$$ is correct.Mathematics

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