2 triangles are congruent if there is a series of rigid transformations that maps one into the other.
The correct answer is rigid transformations. When two triangles are congruent, it means that they have the same shape and size. In order to map one triangle onto another, a series of rigid transformations can be used. Rigid transformations are transformations that do not change the shape or size of an object. These transformations include translations (sliding), rotations (turning), and reflections (flipping). By applying these transformations in a specific sequence, one triangle can be mapped exactly onto the other, proving their congruence. Dilation, on the other hand, is a transformation that changes the size of an object, so it would not be appropriate for establishing congruence between triangles.
