In the diagram below of \(\triangle ABC\) and \(\triangle DEF\), \(\angle CAB = \angle FDE\), and \(AC = DF\). To prove that \(\triangle ABC\) and \(\triangle DEF\) are congruent by ASA, what other information is needed? \(\overline{AB} \cong \overline{DE}\) \(\angle ACB \cong \angle DFE\) \(\overline{BC} \cong \overline{EF}\) \(\angle ABC \cong \angle DFE\)
Added by Beatriz S.
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This means that the angle ZDFE is congruent to the angle ZACB. So, we have ZABC = ZDFE. Show more…
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$$\begin{array}{c} \text { Given: } \mathrm{AB}=\mathrm{DE}, \mathrm{BC}=\mathrm{EF} \\ \text { and } \mathrm{AC}=\mathrm{DF} \\ \text { Prove: } \quad \triangle \mathrm{ABC} \cong \triangle \mathrm{DEF} \end{array}$$ To prove the triangles congruent, we will draw a third triangle and show that $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are both congruent to it. $$\begin{array}{c} \mathrm{AB}=\mathrm{DE}, \mathrm{BC}=\mathrm{EF}, \text { and } \\ \mathrm{AC}=\mathrm{DF} \end{array}$$ Given.
Congruent Triangles
The S.S.S. Congruence Theorem
$$\begin{array}{c} \text { Given: } \mathrm{AB}=\mathrm{DE}, \mathrm{BC}=\mathrm{EF} \\ \text { and } \mathrm{AC}=\mathrm{DF} \\ \text { Prove: } \quad \triangle \mathrm{ABC} \cong \triangle \mathrm{DEF} \end{array}$$ To prove the triangles congruent, we will draw a third triangle and show that $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are both congruent to it. $$\triangle \mathrm{APC} \cong \triangle \mathrm{DEF}$$ S.A.S. postulate. (GRAPH CANT COPY)
$$\begin{array}{c} \text { Given: } \mathrm{AB}=\mathrm{DE}, \mathrm{BC}=\mathrm{EF} \\ \text { and } \mathrm{AC}=\mathrm{DF} \\ \text { Prove: } \quad \triangle \mathrm{ABC} \cong \triangle \mathrm{DEF} \end{array}$$ To prove the triangles congruent, we will draw a third triangle and show that $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are both congruent to it. $$\text { Draw } \overline{\mathrm{CP}} \text { . }$$ (GRAPH CANT COPY)
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