Question

If a transversal intersects two parallel lines prove that the bisector of any pairs of corresponding angles so formed are parallel

Answer 1

Let AB ║ CD and 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.
 Since the corresponding angles of parallrl lines are equal,
∴∠EPB = ∠PQD
∴1/2 ∠EPB = 1/2 ∠PQD
∴∠EPR = ∠PQS
 But they are corresponding angles of PR and QS
Since the corresponding angles are equal
∴ PR ║ QS

Answer 2

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ŸØÚŘ answer is in above attachment...

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