Plz help,

In the figure, PQRS is a quadrilateral & T & U are respectively points on PS & RS such that PQ = RQ, /_PQT = /_RQU & /_TQS = /_UQS. Prove thart QT = QU

Given, PQ =  RQ,

∠PQT = ∠RQU and

∠TQS = ∠UQS

To prove: QT = QU

Proof:

In ΔPQS and ΔRQS, we have

PQ = RQ [Given]

QS = QS [Common]

⇒ ΔPQS ΔRQS [SAS congruency]

⇒ ∠PSQ = ∠QSR [c.p.c.t]

or ∠TSQ = ∠USQ

Again, in ΔTQS and ΔSQU, we have

∠TQS = ∠SQU [Given]

QS = QS [Common]

and ∠TSQ = ∠QSU

⇒ ΔTQS ΔSQU [ASA congruency]

⇒ QT = QU [c.p.c.t]