In this figure BC is based on ABC and DBC Triangles . so we need to prove <ABD = <ACD
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In triangle ABC
AB=AC
angle ABC=angle ACB ---------(1)
In triangle BCD
BD=CD
angle DBC=angle DCB --------------(2)
Adding (1) and (2) we get
ABC+DBC=ACB+ DCB
angle ABD=angle ACD
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