Q. 3

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

Let us draw the figure as below –

The two parallel lines are PR and QT.

Line A intersects P and Q at points C and D respectively.

Let CB and DE be the bisectors of ACR and ADT respectively.

We have to prove that CB and DE are parallel to each other.

We know, if two lines are parallel to each other, the corresponding angles are equal.

Dividing both sides by 2,

Now, we have two lines CB and DE such that the corresponding angles, ACB and CDE are equal.

Thus, CB || DE

Therefore, it is proved that the bisectors of any pair of corresponding angles so formed are parallel.

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