## Elementary Geometry for College Students (5th Edition)

Using SSS for 3 congruent pairs of sides, we can show that $\triangle ABC\cong\triangle DBC$.
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, $\triangle ABC\cong\triangle DBC$.