Question

A transversal intersects 2 parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

Answer 1

Step-by-step explanation:

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