In Fig. AD=BC and BD=CA. Prove that ∠ADB=∠BCA and ∠DAB=∠CBA
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Solution
In triangles ABD and BAC, we have
AD = BC [Given]
BD = CA [Given] and AB = AB [Common]
So, by SSS congruence criterion, we have △ABD≅BAC⇒∠DAB=∠CBA[∵ corresponding parts of congruent triangles are equal] ⇒∠ADB=∠BCA