Question

In the given figure, $RS=QT$ and $QS=RT.$ Prove that $PQ=PR$

Answer 1

Let $QS$ $RT$ meet at $U$

Consider $△RUS$ and $△QUT$

$RS=QT$

$QS=RT$

$\angle RUS=\angle QUT$

$⟹△RUS,△QUT$ are congruent

Consider $△PRT$ and $△PQS$

$\angle PRT=\angle PQS$

$\angle RTP=\angle QSP$

$RT=SQ$

$⟹△PRT,△PQS$ are congruent

$⟹PQ=PR$