Question

14. If two straight lines 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

Answer:

geometric gestures of whatecerrbkskbkaig

Answer 2

Step-by-step explanation:

Brainly.in

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vi9pata5saipra

vi9pata5saipra

21.08.2016

Math

Secondary School

+8 pts

Answered

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.

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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.

∠ AOP = ∠ BOQ (vertically opposite angles)

∠ COP = ∠ DOQ (vertically opposite angles)

∠ AOP = ∠ COP (OP is the bisector of ∠ AOC)

∴ ∠ BOQ = ∠ DOQ

Thus, the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

Similarly, the bisector of ∠ AOD also bisects the ∠ BOC.