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Question 3
AP an BQ are the bisectors of the two alternate interior angles formed by the intersection of a transversal t with parallel lines l and m (in the given figure). Show that AP || BQ.

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Solution

Given, 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.
EAB=ABH [alternate interior angles]

12 EAB=12 ABH [divided both sides by 2]
PAB=ABQ
[AP and BQ are the bisectors of EAB and ABH]
Since, PAB and ABQ are alternate interior angles angles with two lines AP and BQ and transversal AB.
Hence, AP || BQ.

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