# 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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