Question

PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.

Prove that: QR = QT

Answer 1

∠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.