Login

Prove that if a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

Dear Student
The solution of your asked query is provided below:

Theorem 6.2 of class IX of mathematics states that alternate interior angles are equal. and proof of theorem 6.2 is provided below:
The figure is shown below,

Given: EF and CD are parallel, and AB is transversal.To proof:1)∠EGH =∠GHD2)and ∠FGH =∠GHC1)∠AGF =∠EGH (vertically opposite angle)and ∠AGF =∠GHD (corresponding angles)Equating above these two angle we get,so ∠EGH =∠GHD (hence proved)2) ∠BHD =∠GHC (vertically opposite angle)and ∠BHD =∠FGH (corresponding angle)Equating above these two angle we getSo ∠GHC =∠FGH (hence proved)

Hope this information clears your doubt about the topic.
Regards

  • 2
View Full Answer
\\\\\
  • 1

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

             is the transversal.

            AB and  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.

 

         


  • 1
What are you looking for?