Q. 184.0( 4 Votes )
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
In △AOD and △COB
∠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
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