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Question

If Fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such PQ = RQ.
PQT = RQU and TQS = UQS. Prove that QT = QU. 
[4 MARKS]


Solution

Concept : 1 Mark
Process : 2 Marks
Proof : 1 Mark

We have,

PQT = RQU and, TQS = UQS

 PQT + TQS = RQU + UQS  [Adding both angles]

PQS = RQS..........(i)

Thus, In Δ PQS and Δ RQS,
PQ = RQ     [Given]
PQS = RQS    [From (i)]
and, QS = QS     [Common side]

Δ PQS Δ RQS [SAS congruence criterion]

QPS = QRS  [C.P.C.T.C]

QPT = QRU............(ii)

Now, In  Δ QPT and Δ QRS,
QP = QR     [Given]
PQT = RQU     [Given]
QPT = QRU     [From (ii)]

 ΔQPT ΔQRU
QT = QU

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