# In the given figure, PQ > PR and QS and RS are the bisectors of ∠Q and

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:

$P Q>P R$

$\Rightarrow \angle R>\angle Q$

$\Rightarrow \frac{1}{2} \angle R>\frac{1}{2} \angle Q$

$\Rightarrow \angle S R Q>\angle R Q S$

$\Rightarrow Q S>S R$

$\therefore S Q>S R$