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Question 3
A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

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Solution

Given, two lines AB and CD are parallel and intersected by transversal t at P and Q respectively. Also, EP and FQ are the bisectors of angles APG and CQP, respectively.

To prove: EP||FQ
Proof:
Given, AB || CD.
APG=CQP [corresponding angles]
12 APG=12CQP [dividing both sides by 2]
EPG=FQP
[ EP and FQ are the bisectors of APG and CQP respectively]
These are the corresponding angles on the transversal line t.
EP || F Q
Hence, proved.


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