1. 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.
2. In triangles \(ABC\) and \(DEF\), \(\angle A = \angle D\), \(\angle B = \angle E\) and \(AB = EF\). Will the two triangles be congruent? Give reasons for your answer.
Solution:
1. We know that if two sides of two triangles are equal, their common angle is equal.
Here, \(\angle A = \angle \)
By congruence rule, the triangles \(ABC\) and \(EDF\) are congruent.
2. In \(\triangle ABC\), the two angles and the side included are given.
Similarly, in \(\triangle DEF\), the angles are equal, but the side is not included in the given angle.
Hence, the two triangles, \(ABC\) and \(DEF\), are not congruent because \(AB\) and are not the corresponding sides in the two triangles.