Final answer:
A transformation that always preserves congruence and orientation is called a rigid motion or isometry, which includes rotations. Regarding a cube, rotations around the C4 and C3 axes maintain the cube's original appearance and properties.
Step-by-step explanation:
The transformation that always preserves both congruence and orientation is known as a rigid motion or isometry. These transformations include translations, rotations, and reflections. In the context of a cube, a rotation that preserves the cube's appearance is one example of a rigid motion. When discussing rotations that leave a cube's appearance unchanged, there are specific axes around which these rotations can occur. For instance, the cube has three mutually perpendicular four-fold rotational axes (C4 axes), which allow 90° rotations. Additionally, cubes have three-fold or C3 axes, which permit 120° rotations. Both types maintain the cube's congruence and orientation, which means the shape and the direction of points remain consistent before and after the transformation.