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Question
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: QR = QT
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Solution
∠PST = ∠TSR ............(i)
∠PTS = ∠TSR ............(ii)(alternate angles ∵ SR || PQ)
From (i) and (ii)
∠PST = ∠PTS
Therefore,
PT = PS
But PT = QT ...(T is midpoint of PQ)
And PS = QR ...(PS and QR are opposite and equal sides of a parallelogram)
Hence,
QT = QR.
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