Question

If a transversal intersects such that the the bisectors of a pair of alternate interior angles are parallel, then prove that the two lines are parallel.​

Answer 1

As the bisector of alternate interior angles parallel , so the alternate interior angles are equal. As the alternate interior angles are equal,so the lines are parallel .

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Answer 2

Answer:

Given:

AB parallel to CD

EF is the transversal

PR and QS are the bisectors of angle EPB and Angle PQD

To Prove:

PQ parallel to QS

Proof:

Angle EPB = Angle PQD

So, 1/2 angle EPB = 1/2 angld PQD

Therefore, angle EPR = angle PQS

But they are corresponding angles of PR and QS.

Since, the corresponding angles are equal.

PR IS PARALLEL TO QS.

Hence , Prooved.

Refer the attachment.

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