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We have ∠1=∠2 and ∠3=∠4
⇒∠1+∠3=∠2+∠4
⇒∠ACD=∠BDC.
Thus in triangles ACD and BDC, we have,
∠ADC=∠BCD (given);
CD = CD (common);
∠ACD=∠BDC (proved).
By ASA condition △ACD≅△BDC. Therefore
AD=BC and ∠A=∠B.
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