Question

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

Answer 1

OA.OB = OC.OD (Given) ... (1)

Also we have ∠AOD = ∠COB

(vertically opposite angles) … (2)

From (1) and (2)

∴ ΔAOD ~ ΔCOB (SAS similarity criterion)

So, ∠A = ∠C and ∠B = ∠D

(corresponding angles of similar triangles)