Let,
AB ║ CD
EF be the transversal passing through the two parallel lines at P and Q respectively.
PR and QS are the bisectors of ∠EPB and ∠PQD.
We know that the corresponding angles of parallel lines are equal,
So, ∠EPB = ∠PQD
½ ∠EPB = ½ ∠PQD
∠EPR = ∠PQS
But, we also know that they are corresponding angles of PR and QS
Since the corresponding angles are equal,
We have,
PR ║ QS
Hence Proved.