Question

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

Answer 1

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 ∠EGB= 1/2 ∠GHD

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⇒∠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.