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

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

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Given: A transversal EF cuts two parallel lines AB and CD at points G & H. GL and HM are bisectors of angles

To prove: GL \parallel HM
Proof: \angle EGB = \angle GHD (Corresponding angles)
\frac{1}{2} \angle EGB =\frac{1}{2} \angle GHD

\angle EGL = \angle GHM
These are the corresponding angles formed by the line GL and HM, where EF is the transversal.

\therefore GL \parallel HM

Hence proved

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