Question

2 AB parallel to CD. EH is the transversal. PF is the bisector of angle AFG. GQ is the bisector of angle FGD
Are PF and GQ parallel?
Give reason​

Answer 1

Step-by-step explanation:

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.