Question

In the given figure, PQRS is a quadrilateral. If QS is
the angle bisector of angle PQR and angke PSR. Show that
triangle PQS is congruent to triangle RQS. Also prove that PS = RS.​

Answer 1

Answer:

QS = QS (commom side)

RQS = PQS

PSQ = RSQ

therfore triangle PQS = RQS

Answer 2

Step-by-step explanation:

In △PQS and △RQS

∠PQS=∠RQS (QS bisects the angle ∠PQR)

∠PSQ=∠RSQ (QS bisects the angle ∠PSR)

QS=QS (common)

∴ △PQS ≅ △RQS (By AAS)

∴PS=RS (By CPCTC)

Hence proved