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 a 90-degree rotation.
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.

Explanation:

To determine the rotations that map a square onto itself, we analyze rotational symmetry. A square has rotational symmetry of order 4, meaning it can be rotated by multiples of \( \frac{360^\circ}{4}=90^\circ \) and still map onto itself. So rotations of \( 90^\circ \), \( 180^\circ \) (which is \( 2\times90^\circ \)), \( 270^\circ \) (which is \( 3\times90^\circ \)), and \( 360^\circ \) (which is \( 4\times90^\circ \), a full rotation) will all map the square onto itself.

• Option A is incomplete as it doesn't mention the other valid rotations.
• Option C is incomplete as it only mentions \( 180^\circ \) and ignores \( 90^\circ \), \( 270^\circ \), and \( 360^\circ \).
• Option D is incomplete as it ignores \( 270^\circ \) and \( 360^\circ \).
• Option B includes all the valid rotational angles for the square to map onto itself.

Answer:

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