Question

If two parallel lines are intersected by a transversal, show that the bisectors of any corresponding angles are parallel

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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)

⇒21∠EGB=21∠GHD

⇒∠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.