Final answer:
Triangle ABC can be congruent to triangle A'B'C' if it has been transformed via a rotation or a reflection, as both are considered rigid transformations that preserve the size and shape of geometric figures. The correct answer is option O no, because a rotation is not a rigid transformation
Step-by-step explanation:
To determine whether triangle ABC is congruent to triangle A'B'C', one must know the transformation that maps one triangle onto the other. In the context of rigid transformations, if triangle ABC is transformed into triangle A'B'C' through either a rotation or a reflection, then the two triangles are indeed congruent. Rigid transformations, which include reflections and rotations, preserve the size and shape of geometric figures. Consequently, the corresponding sides and angles of the original and image figures remain equal.
Congruent triangles resulting from rigid transformations maintain all their corresponding sides and angles equal. A rotation of a figure is a transformation that turns the figure around a fixed point without changing its size or shape. Since it is a rigid transformation, it preserves congruency. Similarly, a reflection over a line (mirror line) also results in a congruent figure since it is the flip of the figure over the line, once again preserving size and shape.
In conclusion, if triangle ABC has been transformed to triangle A'B'C' via a rotation or a reflection, then triangle ABC is congruent to triangle A'B'C' because both rotations and reflections are rigid transformations that do not alter the size or shape of geometric figures.