Question

If two straight line intersect each other then prove that the ray opposite to the bisector of one of the angles so formed bisects the vertically opposite angle.​

Answer 1

Given AB and CD are straight lines which intersect at O. OP is the bisector of ∠AO.

To prove: OQ is the bisector of ∠BOD.

Proof: AB, CD and PQ are straight lines which intersect in O.

∠AOP=∠BOQ(vertically opposite angles)

∠COP=∠DOQ(vertically opposite angles)

∠AOP=∠COP(OP is the bisector of ∠AOC)

∴∠BOQ=∠DOQ

Thus, the rate opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle. Similarly, the bisection of ∠AOD also bisects the ∠BOC.