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 60 - degree rotation.
a square will rotate onto itself after a 60 - degree or 180 - degree rotation.

Explanation:

Step1: Recall square's rotational symmetry

A square has 4 - fold rotational symmetry.

Step2: Analyze rotation angles

The angles of rotation that map a square onto itself are $\frac{360^{\circ}}{n}$, where $n$ is the number of times it can be rotated onto itself. For a square, $n = 4$. So the angles are $90^{\circ},180^{\circ},270^{\circ},360^{\circ}$.

Answer:

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