Question

If the bisectors of a pair of corresponding angles formed by a transversal with two given lines

are parallel, prove that the given lines are parallel.​

Answer 1

Answer:

Given: AB and CD are two straight lines cut by a transversal EF at G and H respectively. GM and HN are the bisectors of corresponding angles ∠EGB and ∠GHD respectively such that GM∥HN.

To Prove: AB∥CD

Proof:

∵GM∥HN

∴∠1=∠2 (Corresponding angles)

⇒2∠1=2∠2⇒∠EGB=∠GHD⇒AB∥CD

(∠EGB & ∠GHD are corresponding angles formed by transversal EF with AB and CD and are equal.)

Hence, proved.