Question

If $PQ=PR$, Show that $PS>PQ$.

Answer 1

Solution:-

Given : PSR is a triangle.and PQ = PR

To prove:- $PS>PQ$

Proof :

In $△PQR$,

$PQ=PR$

$\therefore \angle PQR=\angle PRQ(\because \text{Angles opposite to equal sides are equal})$

Now,

$\angle PQR>\angle PSQ(\because \text{exterior angle of a triangle is always greater than each of its interior angles.})$

$\Rightarrow \angle PRQ>\angle PSQ(\because \angle PQR=\angle PRQ)$

$\Rightarrow \angle PRS>\angle PSR$

now in $△PSR$,

$\angle PRS>\angle PSR$

$\therefore PS>PR$

$\Rightarrow PS>PQ(\because PQ=PR)$

Hence proved.