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Proving Congruent Triangles

Proving Congruent Triangles 1.9 - Solution

arrow_back Return to Proving Congruent Triangles

We are asked which postulate or theorem we could use to prove ABCDEF.\triangle{ABC} \cong \triangle{DEF}.

It is given that AD,ACDF,\angle{A} \cong \angle{D},\, \overline{AC} \cong \overline{DF}, and CF.\angle{C} \cong \angle{F}. Therefore, two angles and the included side of ABC\triangle{ABC} are congruent to two angles and the included side of DEF.\triangle{DEF}. Therefore, we can conclude that ABCDEF\triangle{ABC} \cong \triangle{DEF} by the Angle-Side-Angle Congruence Theorem. {ADACDFCFABCDEF by ASA\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}