If two straight lines intersect each other, prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

Question

Philoid · Accepted Answer

Given that,

AB and CD intersect at O

OF bisects ∠COB

To prove: ∠AOF = ∠DOF

Proof: OF bisects ∠COB

∠COE = ∠EOB = x (Vertically opposite angle)

∠BOE = ∠AOF = x (i)

∠COE = ∠DOF = x (ii)

From (i) and (ii), we get

∠AOF = ∠DOF = x

Hence, proved