The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.
Let [tex]${data-answer}amp;\overline{A B} \cong \overline{D E} \\[/tex] and [tex]${data-answer}amp;\overline{A C} \cong \overline{D F}[/tex]
Angle between [tex]$\overline{A B}$[/tex] and [tex]$\overline{A C}$[/tex] exists [tex]$\angle A$[/tex].
Angle between [tex]$\overline{D E}$[/tex] and [tex]$\overline{D F}$[/tex] exists [tex]$\angle D$[/tex].
Therefore, [tex]$\triangle A B C \cong \triangle D E F$[/tex] by SAS, if [tex]$\angle A \cong \angle D$[/tex].
Given:
[tex]${data-answer}amp;\overline{A B} \cong \overline{D E} \\[/tex] and
[tex]${data-answer}amp;\overline{A C} \cong \overline{D F}[/tex]
According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.
Let [tex]${data-answer}amp;\overline{A B} \cong \overline{D E} \\[/tex] and [tex]${data-answer}amp;\overline{A C} \cong \overline{D F}[/tex]
Angle between [tex]$\overline{A B}$[/tex] and [tex]$\overline{A C}$[/tex] exists [tex]$\angle A$[/tex].
Angle between [tex]$\overline{D E}$[/tex] and [tex]$\overline{D F}$[/tex] exists [tex]$\angle D$[/tex].
Therefore, [tex]$\triangle A B C \cong \triangle D E F$[/tex] by SAS, if [tex]$\angle A \cong \angle D$[/tex].
To learn more about SAS congruence property refer to:
https://brainly.com/question/19807547
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