Why do translation reflections and rotation create congruent images?

Translation, reflection, and rotation are all rigid transformations, meaning they preserve the shape and size of geometric figures. When a shape is translated, reflected, or rotated, its dimensions, angles, and relative positions remain unchanged, resulting in congruent images. This congruence ensures that the original figure and its image are identical in terms of size and shape, allowing for a perfect overlay when aligned properly. Thus, these transformations maintain the fundamental properties of the shapes involved.