1.

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

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Answer:

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.

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