Question

ray oc is the bisector of aob and od is the ray opposite to oc.show that aod=bod?​

Answer 1

Given :   ray oc is the bisector of aob and od is the ray opposite to oc

To find : show that aod=bod

Solution:

ray oc is the bisector of aob

=> ∠AOC = ∠BOC = ∠AOB/2

od is the ray opposite to oc  

=> CD is a straight line

=> ∠AOC +  ∠AOD = 180°

=> ∠AOB/2 + ∠AOD = 180°

=>  ∠AOD = 180° - ∠AOB/2

CD is a straight line

= ∠BOC +  ∠BOD = 180°

=> ∠AOB/2 + ∠BOD = 180°

=>  ∠BOD = 180° - ∠AOB/2

=> ∠AOD = 180° - ∠AOB/2 = ∠BOD

=> ∠AOD =  ∠BOD

QED

Hence Proved

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