Question

If a transversal intersects two parallel lines then each pair of corresponding angles is equal proof

Answer 1

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Answer 2

Statement: If a transversal intersects two parallel lines then each pair of corresponding angles is equal.

Given: Lines are parallel

              AB║CD

To Prove: Corresponding angles are equal

                    ∠1 = ∠3

                    ∠2 = ∠4

                    ∠5 = ∠7

                    ∠6 = ∠8

Proof:  AB║CD

            $l$ is the transversal.

            AB and $l$ are intersecting lines.

           ⇒ ∠1 = ∠6           [∵ vertically opposite angles ]  -----------(1)

               ∠6 = ∠3           [∵ alternate interior angles]    ------------(2)

           From (1) and (2)

               ∠1 = ∠3

           Similarly, we can prove that

               ∠2 = ∠4

                ∠5 = ∠7

                ∠6 = ∠8

           ∴ All four pairs of corresponding angles are equal when a transversal intersects two parallel lines.