Answer
Using SSS for 3 congruent pairs of sides, we can show that $\triangle ABC\cong\triangle DBC$.
Work Step by Step
It is given that
1) $\overline{AC}\cong\overline{CD}$
2) $\overline{AB}\cong\overline{BD}$
3) $\overline{CB}\cong\overline{CB}$ (by Identity)
Therefore, now we have 3 sides of $\triangle ABC$ are congruent with 3 sides of $\triangle DBC$. So, according to SSS, $\triangle ABC\cong\triangle DBC$.
