\(ABC\) and \(DBC\) are two isosceles triangles on the same base \(BC\). Show that \(∠ ABD = ∠ ACD\).
 
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Proof:  
 
In \(\triangle DAB\) and \(\triangle DAC\), 
 
\(\triangle DAB \cong \triangle DAC\) [By Congruence rule]
 
Then, \(∠ABD = ∠ACD\) [By]
 
Hence, we proved.