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We are asked which postulate or theorem we could use to prove $\triangle{ABC} \cong \triangle{DEF}.$
It is given that $\angle{A} \cong \angle{D},\, \overline{AC} \cong \overline{DF},$ and $\angle{C} \cong \angle{F}.$ Therefore, two angles and the included side of $\triangle{ABC}$ are congruent to two angles and the included side of $\triangle{DEF}.$ Therefore, we can conclude that $\triangle{ABC} \cong \triangle{DEF}$ by the Angle-Side-Angle Congruence Theorem. $\begin{gathered} \begin{cases}{\color{#0000FF}{\angle{A} \cong \angle{D}}} \\ {\color{#009600}{\overline{AC} \cong \overline{DF}}} \\ {\color{#FF0000}{\angle{C} \cong \angle{F}}} \end{cases} \quad \Rightarrow \quad \triangle{ABC} \cong \triangle{DEF} \text{ by }{\color{#0000FF}{\text{A}}}{\color{#009600}{\text{S}}}{\color{#FF0000}{\text{A}}} \end{gathered}$