In figure AP $\perp \ell$ i.e., AP is the shortest line segment that can be drawn from A to the line $\ell$. If  $PR>PQ$ then 

Cut off $PS=PQ$ from $PR$ join AS

In $\Delta APQ \& \Delta APS$

$\begin{array}{l}\angle APQ=\angle APS,AP=AP,PQ=PS\\ \therefore \Delta APQ\cong \Delta APS\\ AQ=AS\&\left(1\right)=\left(3\right)\to \left(1\right)\\ In\Delta ARS,\left(3\right)>\left(2\right)\to \left(2\right)\\ From\left(1\right)\&\left(2\right),\left(1\right)>\left(2\right)\\ AR>AQ\end{array}$