Answer
Using method ASA with 2 congruent pair angles and 1 congruent pair of included sides, we can prove that $\triangle ABC\cong\triangle DBC$.
Work Step by Step
It is given that
1) $\angle A\cong\angle D$
2) $\overline{AB}\cong\overline{BD}$
3) $\angle 1\cong\angle 2$
2 angles of $\triangle ABC$ are congruent with 2 angles of $\triangle DBC$ and 1 included side of $\triangle ABC$ is congruent with 1 included side of $\triangle DBC$.
Therefore, according to method ASA, $\triangle ABC\cong\triangle DBC$.
