Question

In Fig. PQ > PR. QS and RS are the bisectors of $\angle$Q and $\angle$R respectively

Prove that SQ>SR

Answer 1

In $△$ PQR, we have

PQ > PR [Given]

$\Rightarrow$ $\angle$PRQ > $\angle$PQR [Angle opposite to largest side of a triangle is greater]

$\Rightarrow$ $\angle$PRQ > $\angle$PQR

$\Rightarrow$ $\angle$SRQ > $\angle$SQR

[$\because$ RS and QS are bisectors of $\angle$PRQ are $\angle$PQR respectively]

$\Rightarrow$ SQ > SR

[$\because$ Side opp. to greater angle is larger]