In the two triangles $ABC$ and $DEF$,$AB = DE$ and $AC = EF$. Name two angles from the two triangles that must be equal so that the two triangles are congruent. Give reason for your answer.
(A) To prove that $\triangle ABC \cong \triangle DEF$ (or a variation thereof) using the $SAS$ (Side-Angle-Side) congruence criterion,the angle must be included between the two given sides.
For $\triangle ABC$,the sides are $AB$ and $AC$,so the included angle is $\angle A$.
For $\triangle DEF$,the sides are $DE$ and $EF$,so the included angle is $\angle E$.
Therefore,if $\angle A = \angle E$,then by the $SAS$ congruence rule,$\triangle ABC \cong \triangle DEF$.
For $\triangle ABC$,the sides are $AB$ and $AC$,so the included angle is $\angle A$.
For $\triangle DEF$,the sides are $DE$ and $EF$,so the included angle is $\angle E$.
Therefore,if $\angle A = \angle E$,then by the $SAS$ congruence rule,$\triangle ABC \cong \triangle DEF$.
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