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<Sorry, I cannot upload the figure. Kindly draw the figure, before analysing the answer> Given l||m p is the transversal To prove: PQRS is a rectangle Proof: RS, PS, PQ and RQ are bisectors of interior angles formed by the transversal with the parallel lines.

∠RSP = ∠RPQ (Alternate angles) Hence, RS||PQ Similarly, PS||RQ (since ∠RPS = ∠PRQ) Therefore, the quadrilateral PQRS is a parallelogram (as both the pairs of opposite sides are parallel).

From the figure, we have ∠b + ∠b + ∠a + ∠a = 180° ⇒ 2(∠b + ∠a) = 180° ∴ ∠b + ∠a = 90° That is PQRS is a parallelogram with an angle as a right angle. Hence, PQRS is a rectangle.