Question

If two parallel lines are intersected by a transversal then prove that the bisectors of any pair of alternate interior angles are parallel.​

Answer 1

Answer:

Given :- Two parallel lines AB and CD and transversal EF intersects them at G and H respectively. GM and HN are the bisectors of the alternate angles AGH and GHD.

To prove :- GM ll HN.

Proof :- Since AB ll CD and transversal EF cuts them at G and H respectively. Therefore,

AGH = GHD

1/2 ∠GHD = 1/2 ∠EGB  

⇒ MGH = GHN

Thus, two lines and HN are intersected by a transversal GH at G and H respectively such that a pair of alternate angles are equal.

Hence, GM ll HN.