If two angles and a non-included side of a triangle are congruent with two angles and a non-included side of another triangle, then the triangles are congruent (figures).

The triangles above are congruent because ${\textstyle \ang A}$ and ${\textstyle \ang B}$ are congruent with ${\textstyle \ang D}$ and ${\textstyle \ang E,}$ respectively, and $\overline{BC}$ is congruent with $\overline{EF}.$ $$\begin{array}{c}\{\begin{array}{l}\angle A\cong \angle D\\ \angle B\cong \angle E\\ \overline{BC}\cong \overline{EF}\end{array}\Rightarrow △ABC\cong △DEF\end{array}$$