Question

please answer these questions​

Answer 1

Answer:

Given l||m and 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||PQSimilarly, PS||RQ (∠RPS = ∠PRQ)

Therefore 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 and one of the angle is a right angle.

Hence PQRS is a rectangle.

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