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Question
In the following figure, bisectors AP and BQ of the alternate interior angles are parallel, then show that l ||m.
Solution
Given, In the following figure AP || BQ, AP and BQ are the bisectors of alternate interior angles ∠CAB and ∠ABF.
To show l || m
Proof Since, AP || BQ and t is transversal, therefore ∠PAB = ∠ABQ ...[Alternate interior angles]
⇒ 2∠PAB = 2∠ABQ ...[Multiplying both sides by 2]
∠CAB = ∠ABF
So, alternate interior angles are equal.
We know that, if two alternate interior angles are equal, then lines are parallel.
Hence, l || m.
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