Question

$Q$ is a point on side RS of $\Delta PSR$ such that $PQ=PR$ then which of the following is correct:

• A. $PS=PQ$
• B. $PS>PQ$
• C. $PS<PQ$
• D. Cannot be determined

Answer 1

The correct option is B $PS>PQ$

In $\Delta PQR$,

side $PQ=$ side $PR$ ....given

$\angle PQR=\angle PRQ$ ....isosceles triangle theorem
Now, $\angle PQS+\angle PQR={180}^o$ ....angles in linear pair

Since, $\angle PQR$ is an acute angle, $\angle PQS$ is obtuse.

i.e.$m\angle PQS>{90}^o$
Now in $\Delta PQS$,

$m\angle PQS>m\angle PSQ$

$\therefore PS>PQ$
$\therefore PS>PR$ ...($\because PQ=PR$)