What properties remain unchanged during a rotation transformation?

When a rotation transformation is applied to a figure, certain properties of the figure remain unchanged. Specifically, the lengths of sides and the angles between those sides do not change during a rotation. This means that the overall shape and size of the figure are preserved, regardless of how the figure is oriented in the plane.

During a rotation, each point in the figure moves around a fixed point (the center of rotation) at a constant distance and angle. Since the distances between points (lengths of sides) and the measures of angles remain constant, the fundamental characteristics of the figure do not alter. This preservation of properties is a key characteristic of rigid transformations, such as rotations, reflections, and translations.

In contrast, other options incorrectly imply changes to the figure's properties. Only angles or only lengths changing would contradict the nature of a rotation, as both the angles and lengths must remain constant. Additionally, the notion that all properties change is not aligned with the definition of rotation, further affirming that lengths and angles indeed stay the same during this transformation.