Question

26. PQRS is a quadrilateral. T and U are points on PS and RS respectively such that
PQ=RQ, ZPQT = ZRQU and ZTQS = ZUQS. Then
a) QT' = TU
b) QU = TU
c) QT = QU
d) None of these​

Answer 1

Answer:

c) QT = QU

Step-by-step explanation:

PQ=RQ, (Given)

ZPQT = ZRQU (Given)

ZTQS = ZUQS (Given)

In ΔPQS and ΔRQS, we have

PQ = RQ

QS = QS [Common line]

∠PQS = ∠ RQS

Thus,  ΔPQS ~ ΔRQS [SAS congruent]

= ∠PSQ = ∠QSR  

or ∠TSQ = ∠USQ

In, ΔTQS and ΔSQU, we have

∠TQS = ∠SQU

QS = QS [Common line]

and ∠TSQ = ∠QSU

Thus, ΔTQS  ~ ΔSQU [ASA congruent]

Therefore,

QT = QU