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Answer :
In \(\triangle{ABC}\) and \(\triangle{BAC}\), we have
AD = BC ...(Given)
Also,
\(\angle{DAB}\) = \(\angle{CBA}\) ...(Given)
And AB is a common side.
Therefore,
\(\triangle{ABD}\) \(\displaystyle \cong \) \(\triangle{BAC}\) ...(SAS congruency test)
Hence, BD = AC ...(By CPCT)
and \(\angle{ABD}\) = \(\angle{BAC}\) ...(By CPCT)
Hence, proved.