Question

symmetry quick check
which statement best summarizes the rotations that turn a square onto itself? (1 point)
a square will rotate onto itself after 90 - degree, 180 - degree, 270 - degree, and 360 - degree rotations
a square will rotate onto itself after a 180 - degree rotation
a square will rotate onto itself after a 90 - degree or 180 - degree rotation
a square will rotate onto itself after a 90 - degree rotation

Explanation:

Step1: Recall rotation - symmetry of a square

A square has rotational symmetry of order 4. The center of rotation is the intersection of its diagonals.

Step2: Determine the angles of rotation

The angles of rotation that map a square onto itself are found by dividing 360° by the order of rotational - symmetry. Since the order is 4, $\frac{360^{\circ}}{4}=90^{\circ}$. So, rotations of 90°, 180° (which is 2×90°), 270° (which is 3×90°), and 360° (which is 4×90°) will turn a square onto itself.

Answer:

A. A square will rotate onto itself after 90 - degree, 180 - degree, 270 - degree, and 360 - degree rotations