Question

Q is a point on the side SR of a $\Delta PSR$ such that PQ = PR. Prove that PS > PQ.

Answer 1

Given:

$Q$ is a point on side $SR$ in $\Delta PSR$ such that $PQ=PR$

$\Rightarrow PS>PR$ …… (1)

Proof:

In $\Delta PQR$,

$PQ=PR$

$\Rightarrow \angle PQR=\angle PRQ$

Now, from (1)

$\angle PRQ>\angle PSQ$ or $\angle PRS>\angle PSR$

Now, in $\Delta PSR$,

$\angle PRS>\angle PSR$

$\Rightarrow PS>PR$

$\Rightarrow PS>PQ$

Hence, proved.