A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

Please send the answer as soon as possible

Question

A transversal intersects two parallel lines Prove that the
bisectors of any pair of corresponding angles so formed are
parallel
Please send the answer as soon as possible

Gursheen kaur. · Accepted Answer

Given: A transversal EF cuts two parallel lines AB and CD at point G and H resp. GL and HM are the bisectors of a pair of a corresponding angles EGB and GHD resp.

To prove: GL is parallel to HM

Proof: since AB is parallel CD and EF is a transversal

$∴ ∠ E G B = ∠ G H D [c o r r e s p o n d i n g a n g l e s] \Rightarrow \frac{1}{2} ∠ E G B = \frac{1}{2} ∠ G H D \Rightarrow ∠ L G B = ∠ M H D b u t t h e s e a r e c o r r e s p o n d i n g a n g l e s f o r m e d b y l i n e s G L & H M t h e r e f o r e, G L ∥ H M .$

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel. Please send the answer as soon as possible

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

Please send the answer as soon as possible