Question

In the given figure, PQ > PR and QS and RS are the bisectors of ∠Q and ∠R respectively. Show that SQ > SR.

Answer 1

Since the angle opposite to the longer side is greater, we have:

$$\begin{gathered} PQ>PR \\ \Rightarrow \angle R>\angle Q \\ \Rightarrow \frac{1}{2}\angle R>\frac{1}{2}\angle Q \\ \Rightarrow \angle SRQ>\angle RQS \\ \Rightarrow QS>SR \end{gathered}$$

∴$SQ>SR$