Question

In the given figure PQRS is a parallelogram, PQ is produced to U, and T is th emid point of QR . If SR=10, find the length of PU

Answer 1

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 RQ