Final answer:
A square can be rotated by various angles such as 0°, 90°, 180°, and 270° and still map onto itself because of its symmetrical properties. It also has four lines of reflection including the diagonals and bisectors of opposite sides.
Step-by-step explanation:
Understanding Rotations and Reflections in Geometry
When a square is rotated about its center by 360°, it maps onto itself at four different angles of rotation, which are 0°, 90°, 180°, and 270°. These angles are significant because they represent the symmetry of the square. A rotation of 0° corresponds to leaving the square unchanged, a 90° rotation is a quarter turn, a 180° rotation is a half turn, and a 270° rotation is three-quarters of a turn. Additionally, a square can be reflected onto itself across four different lines of reflection. These lines include the two diagonals of the square, as well as the two lines that bisect opposite sides.
Each reflection across these lines will produce a mirror image of the square, but the overall shape and size of the square remain the same. This property of having multiple lines of reflection is also a characteristic of the square's symmetry.