Question

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

Prove that: RT bisects angle R

Answer 1

Since QT = QR
∠QTR = ∠QRT
But ∠QTR = ∠TRS    ...(alternate angles ∵ SR || PQ)
⇒ ∠QRT = ∠TRS
Therefore, RT bisects ∠R.