In the given figure, bisectors `AP` and `BQ` of the alternate interior angles are parallel, then show that `l` `|""|``m`.

Explanation

Given. In the 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 ]
`rArr" " 2/_PAB = 2 /_ABQ " " `[multiplying both sides by 2]

`rArr" "/_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