Question
In figure, EF is a transversal to two parallel lines AB and CD, GM and HL are the bisectors of the corresponding angles EGB and EHD. Prove that GM || HL.
[Hint. First prove that ∠EGM = ∠GHL]
Solution
AB || CD and a transversal EF intersects them
∴ ∠EGB = ∠GHD
| Corresponding Angles
⇒ 2 ∠EGM = 2 ∠GHL
| ∵ GM and HL are the bisectors of ∠EGB and ∠EHD respectively.
⇒ ∠EGM = ∠GHL
But these angles form a pair of equal corresponding angles for lines GM and HL and transversal EF.
∴ GM || HL.
