Question:
In the given figure, PQ > PR and QS and RS are the bisectors of ∠Q and ∠R respectively. Show that SQ > SR.
Solution:
Since the angle opposite to the longer side is greater, we have:
$P Q>P R$
$\Rightarrow \angle R>\angle Q$
$\Rightarrow \frac{1}{2} \angle R>\frac{1}{2} \angle Q$
$\Rightarrow \angle S R Q>\angle R Q S$
$\Rightarrow Q S>S R$
$\therefore S Q>S R$