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ExamnkExample 4(sec Fig. 8.15). Show that the quadrilateral formed by the bisectors of interior anglesTwo parallel lines I and m are intersected by a transversal pis a rectangle. |
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Answer» Given l||m and p is the transversalTo 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 Thanks |
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