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Question

If a traversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel , then P.T. the two lines are parallel.

Solution
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In figure, transversal AD intersects two lines PQ and RS at points B and C respectively.

Ray BE is the bisector of ABQ
So, ABE=EBQ=12(ABQ)

and ray CG is the bisector of BCS
So, BCG=GCS=12(BCS)
and BECG

We should prove that PQRS

Since, BECG and line AD is the transversal,

ABE=BCG ------ Corresponding angles

12(ABQ)=12(BCS)

ABQ=BCS

But, these angles are the corresponding angles formed by transversal AD with PQ and RS

We know that, If a transversal intersects two lines such that the pair of corresponding angles is equal, then lines are parallel to each other.

So, PQRS
Hence Proved.

1035188_1098798_ans_98370632ee0843538336d0b240b8da4a.JPG

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