Question

In the figure, PQRS is a parallelogram. T is the mod point of QR. Prove that - PU = 2PQ​

Answer 1

Step-by-step explanation:

To prove: QO = OR i.e.

ST bisects RQ. Proof: PQRS is a parallelogram. PQ || RS

Now, PQ || RS and transversal QR intersects them

∠1 = ∠2 …(i) (alternate interior angles)

Now PQRS is a parallelogram ⇒ PQ = RS ⇒ QT = RS …(ii)

QT = PQ (given) Thus in ΔQOT and ΔSOR, we have ∠1 = ∠2 [using (i)]

∠3 = ∠4 (vertically opposite angles)

and QT = RS [using (ii)]

ΔQOT = ΔROS (by AAS congruency rule) ⇒

QO = OR ⇒

O is the mid-point of QR ⇒ ST bisects