PQRS is a parallelogram in which PQ is produced to T such that QT=PQ. prove that ST bisects RQ.
We have PQRS is a parallelogram.
PQ = SR [opposite sides of parallelogram are equal]
But PQ = QT [given]
so, SR = QT
Since SR || PT and ST is a transversal
∠RSM = ∠QTM [Alternate interior angles]
In triangle SMR and TMQ
∠SMR = ∠TMQ [alternate interior angles]
∠RSM = ∠QTM [Alternate interior angles]
SR = QT [proved above]
ΔSMR is congruent to ΔTMQ [AAS CRITERIA]
⇒ RM = QM [CPCT]
so, ST bisects RQ.