Question

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if a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel,then prove that two lines are parallel.



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Answer 1

Heya Mate

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Here is your solution:===

In figure : A transversal AD intersects two lines PQ and RS at points B and C respectively. Ray BE is the bisector of <ABQ and ray CG is the bisector of < BC S and BE ||CG.

It is given that ray BE is the bisector of <ABQ.

Therefore,<ABE=1/2<ABQ........(1)

Similarly,ray CG is the bisector of<BCS.

Therefore, <BCG=1/2<BCS. ........(2)

But BE|| CG and AD is the transversal.

Therefore,<ABE=<BCG (Corresponding angles axiom).......(3)

Substituting (1) and (2) in (3),you get

1/2 <ABQ=1/2 <BCS

That is, <ABQ=<BCS

But they are the corresponding angles formed by transversal AD With PQ and RS;and are equal.

Therefore, PQ||RS (Converse of corresponding angles axiom).

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