Question

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

Answer 1

Answer:

Given: AB and CD are two parallel lines and transversal EF intersects then at G and H respectively. GM and HN are the bisectors of two corresponding angles ∠EGB and ∠GHD respectively.

To prove: GM∥HN

Proof:

∵AB∥CD

∴∠EGB=∠GHD (Corresponding angles)

⇒ ∠1=∠2

(∠1 and ∠2 are the bisector of ∠EGB and ∠GHD respectively)

⇒GM∥HN

(∠1 & ∠2 are corresponding angles formed by transversal GH and GM and HN and are equal.)

Hence, proved.

Answer 2

Answer:

given AB and CD are two parallel lines and transversal EF intersects then at G and H respectively GM and HN are the bisectors of two corresponding angles angle EGB and angle GHD respectively

To prove : GM // HN

Proof :AB // CD

angle EGB and angle GHD are equal (by corresponding angle )

1/2angle EGB =1/2angle GHD

angle 1 =angle 2

angle 1 and angle 2 are bisector of angle EGB and angle GHD respectively

GM //HM

hence proved