Question

Question 4
In the given figure, bisectors AP and BQ of the alternate interior angles are parallel, then show that $l||m$.

Answer 1

Given, AP || BQ, AP and BQ are the bisectors of alternate interior angles $\angle CABand\angle ABF$.
To show I||m,
Proof:
Since, AP || BQ and t is transversal, therefore $\angle PAB=\angle ABQ$.
[alternate interior angles]
$\Rightarrow 2\angle PAB=2\angle ABQ$ [multiplying both sides by 2]

$\Rightarrow \angle CAB=\angle ABF$
So, alternate interior angles are equal.
We know that, if two alternate interior angles are equal, then lines are parallel.
Hence, I || m.