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Answer :
In \(\triangle{ABC}\) and \(\triangle{ABD}\), we have,
AC = AD ....(Given)
As, AB bisects \(\angle{A}\),
Therefore, \(\angle{CAB}\) = \(\angle{DAB}\)
Also, AB is a common side,
So, we can say,
\(\triangle{ABC}\) \(\displaystyle \cong \) \(\triangle{ABD}\) ...(by SAS test of congruency)
Also, BC = BD ...(By CPCT)
Hence, proved.