Question -
Answer -
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.