Question

State true or false:

In the figure, given below, $2AD=AB$. $P$ is mid-point of $AB$. $Q$ is mid-point of $DR$ and $PR\parallel BS$, then $AQ\parallel BS$.

• A. True
• B. False

Answer 1

The correct option is A True

Given: $PR\parallel BS$, $P$ is mid point of $AB$ and $Q$ is mid point of $DR$.
Also, $2AD=AB$
$⟹$ $2AD=AP+PB$ .......($AB=AP+PB$)
$⟹$ $2AD=2AP$ .......($P$ is mid point of $AB$, i.e. $AP=PB$)
$⟹$ $AD=AP$
That is, $A$ is mid point of $PD$.

Now, In $△DPR$,
$A$ is mid point of $PD$ and $Q$ is mid point of $DR$.

Thus, by converse of mid point theorem, $AQ\parallel PR$.

Since $PR\parallel BS$,
hence, $AQ\parallel PR\parallel BS$.

Therefore, the given statement is true and option $A$ is correct.