Question

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Answer 1

Step-by-step explanation:

Given:AP and BQ are the bisectors of the two alternate interior angles formed by the intersection of a transversal t with parallel lines I and m (in the given figure).

To find: Show that AP || BQ.

Solution:

We know that when a transversal cuts two parallel lines their alternate interior angles are equal.

$\angle CAB=\angle DBA$

here,

AP and BQ are angle bisectors,

Thus,

$\frac{1}{2}\angle CAB=\frac{1}{2}\angle DBA$

or

$\angle PAB=\angle QBA$

are the alternate interior angles ,which are equal, which is only possible when the lines are parallel,thus AP || BQ.

Hence proved.

Hope it helps you.