Question

Prove that the bisectors of a pair of alternate angles formed by a transversal with two given lines
are parallel, if 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.

Step-by-step explanation:

please mark as the brainliest

Answer 2

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:

According to the question,

∵ GM ∥ HN

∴∠1=∠2 (Corresponding angles)

⇒2×∠1=2×∠2. [2∠1=∠EGB& 2×∠2=∠GHD.]

⇒∠EGB=∠GHD

⇒AB∥CD

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

Hence, proved

____________________________