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.

Question

Filo · Accepted Answer

Let us consider AB and CD as the two lines intersecting at a point O where OE is the ray bisecting ∠BOD and OF is the ray bisecting ∠AOCTo Prove: ∠AOF=∠COFProof: EF is a straight line passing through the point O where OE and OF are tow opposite raysFrom the figure we know that ∠AOF and ∠BOE, ∠COF and ∠DOE are vertically opposite anglesso it can be written as∠AOF=∠BOE and∠COF=∠DOEit is given that ∠BOE=∠DOEso we can write it as ∠AOF=∠COFtherefore it is proved that ∠AOF=∠COF

Question Text	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 Type	Text solution:1
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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.

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