Question

13. Two straight lines intersect each other at a point and thus four angles are formed.
Let's prove that the bisectors of these angles are two perpendicular straight lines.​

Answer 1

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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.

Answer:

Given that, AB and CD intersect at O.

OF bisects ∠COB.

To prove: ∠AOF =∠DOF.

Proof: OF bisects ∠COB [given] (Vertically opposite angle)

∠BOE =∠AOF = x (i)

∠COE =∠DOF = x (ii)

From (i) and (ii),

we get ∠AOF =∠DOF = x.

Hence, proved.

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