Q6 of 115 Page 8

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.

Given that,


AB and CD intersect at O


 


OF bisects ∠COB


 


To prove: ∠AOF = ∠DOF


 


Proof: OF bisects ∠COB


 


∠COE = ∠EOB = x (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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4

In Fig. 8.59, find the value of x.

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If one of the four angles formed by two intersecting lines is a right angle, then show that each of the four angles is a right angle.

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In Fig. 8.60, ray AB and CD intersect at O.


(i) Determine y when x = 60°


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