Page 8 - LN

To prove:  AOC =  BOD and  AOD =  BOC.

Proof:

Ray OA stands on line CD.
Therefore, AOC +  AOD= 180° (Linear pair axiom) (1)

and  AOD +  BOD = 180°(Linear pair axiom) (2)

From (1) and (2), we canwrite

 AOC +  AOD =  AOD +  BOD
⇒ AOC =BOD (By cancelling  AOD from both
sides)

Similarly, it can be proved that AOD= BOC .