If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel

The transversal $A D$ intersects the two lines $P Q$ and $R S$ at points $B$ and $C$ respectively. $B E$ is the bisector of $∠ A B Q$ and $C F$ is the bisector of $∠ B C S$ .
As, $B E$ is the bisector of $∠ A B Q$ , then,
$∠ A B E = \frac{1}{2} ∠ A B Q$
In the same way,
$∠ B C F = \frac{1}{2} ∠ B C S$
Since BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,
$∠ A B E = ∠ B C F$
$\frac{1}{2} ∠ A B Q = \frac{1}{2} ∠ B C S$
$∠ A B Q = ∠ B C S$
Therefore, by the converse of corresponding angle axiom,
$P Q ∥ R S$ .

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