What property allows a figure to be rotated around a point and still look the same?

The property that allows a figure to be rotated around a point and still look the same is known as rotational symmetry. This occurs when a figure can be rotated about a central point by a certain angle (less than a full circle) and the figure appears unchanged. A classic example of this is a star or a regular polygon, where the figure matches its original shape upon rotating it by a specific degree.

In contrast, while the symmetrical property refers to balance and proportion in design, it does not specifically address the way a shape changes under rotation. Point symmetry indicates that for every point in the figure, there is an equivalent point at an equal distance on the opposite side of a central point, but this also does not specifically imply rotation. The isometric property relates to transformations that preserve distance and angles and is broader than the specific definition of rotational symmetry. Thus, the clarification of rotational symmetry highlights its unique characteristic of maintaining the figure's appearance through rotation, making it the correct answer.