Question

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

Prove that: ∠RTS = 90°

Answer 1

∠PST = ∠TSR
∠QRT = ∠TRS
∠QRS + ∠PSR = 180°   ...(adjacent angles of || gm are supplementary)
Multiplying by `(1)/(2)` 

`(1)/(2)∠"QRS" + (1)/(2)∠"PSR" = (1)/(2) xx x180°`

∠TSR + ∠TRS = 90°
In ΔSTR,
∠TSR + ∠RTS + ∠TRS = 180°
90° + ∠RTS = 180°
∠RTS = 90°.