Given: AB and CD are straight lines which intersect at O.
OP is the bisector of ∠AOC.
To Prove : OQ is the bisector of ∠BOD
Proof :
AB, CD and PQ are straight lines which intersect in O.
Vertically opposite angles: ∠AOP = ∠BOQ
Vertically opposite angles: ∠COP = ∠DOQ
OP is the bisector of ∠AOC : ∠AOP = ∠COP
Therefore, ∠BOQ = ∠DOQ
Hence, OQ is the bisector of ∠BOD.