Elementary Geometry for College Students (7th Edition) Clone

Using method SAS for two congruent pairs of sides and one congruent pair of included angle, we can prove that $\triangle ABC\cong\triangle DBC$.
Since B is the midpoint of $\overline{AD}$, the distance from B to A is equal with the distance from B to D. In other words, $\overline{BA}\cong\overline{BD}$. It is also given that - $\angle A\cong\angle D$ - $\overline{AB}\cong\overline{BD}$ Therefore, we have 2 sides and the included angle of $\triangle ABC$ are congruent with 2 sides and the included angle of $\triangle DBC$. So, according to method SAS, $\triangle ABC\cong\triangle DBC$.