Q18 of 95 Page 6

In the given figure, OA .OB = OC.OD, show that: ∠A = ∠C and ∠B = ∠D.

Given: OA × OB = OC × OD

To Prove: A = C and B = D


Now, OA .OB = OC.OD


…(i)


In △AOD and △COB


(from (i))


∠AOD = ∠COB (vertically opposite angles)


∴ △AOD ~ △COB (by SAS similarity criterion)


We know that if two triangles are similar then their corresponding angles are equal.


⇒ A = C and B = D


Hence Proved


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