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Question
AP and BQ are the bisectors of the two alternate interior angles formed by the intersection of a transversal t with parallel lines l and m (Figure). Show that AP || BQ.
Solution
Given In the figure l || m, AP and BQ are the bisectors of ∠EAB and ∠ABH, respectively.
To prove AP || BQ
Proof Since, l || m and t is transversal.
Therefore, ∠EAB = ∠ABH ...[Alternate interior angles]
`1/2 ∠EAB = 1/2 ∠ABH` ...[Dividing both sides by 2]
∠PAB = ∠ABQ ...[AP and BQ are the bisectors of ∠EAB and ∠ABH]
Since, ∠PAB and ∠ABQ are alternate interior angles with two lines AP and BQ and transversal AB.
Hence, AP || BQ.
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