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1 ∠EAB = ∠ABH
1
2 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. (Converse property of Parallel lines)
13. A transversal intersects two parallel lines. Prove that the bisectors of any pair 4
of corresponding angles so formed are parallel.
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.
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