Question

In the given figure, PS = PR. $\angle TPS=\angle QPR$. Then PT = PQ.

• A. True
• B. False

Answer 1

The correct option is A True

Given $PS=PR,\angle TPS=\angle QPR$

we have to prove that $PT=PQ$

$In△PSR,$

$PS=PR\left(given\right)$

$\therefore \angle PSR=\angle PRS-\left(i\right)$

{ Angles opposite to equal sides of a $△le$ are equal}

$\therefore \angle TPS+\angle PTS=\angle QPR+\angle PQR$

(An exterior angle of a $△le$ is equal to the sum of its two interior opposite angle)

$⟹\angle PTS=\angle PQR$

$\therefore \angle PTQ=\angle PQT\therefore PT=PQ$

(sides opposite to equal angles of a $△le$ are equal).