Proving Congruent Triangles

Let's consider the given diagram, paying close attention to the marks on the sides of each triangle.

Examining the diagram in the exercise, we see three pairs of congruent sides. $\begin{gathered} \overline{AB}\cong\overline{BD}, \ \overline{AC}\cong\overline{DE} \quad \text{and} \quad \overline{BC}\cong\overline{BE} \end{gathered}$ Since the three sides of one triangle are congruent to the three sides of the other triangle, then the triangles are congruent by the SSS Congruence Theorem.