Which statement best summarizes the rotations that turn a square onto itself?(1 point)

Question

Responses

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

A square will rotate onto itself after a 90-degree rotation.

Answer 1

The statement that best summarizes the rotations that turn a square onto itself is:

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

This is because a square can indeed be rotated by these angles (90°, 180°, 270°, and a full 360° rotation) and still look the same as it did in its original position.

Answer 2

What is the smallest degree measure for a regular nonagon to rotate onto itself?(1 point)
Responses

30°
30 degrees

60°
60 degrees

80°
80 degrees

40°

Answer 3

The smallest degree measure for a regular nonagon (which has 9 sides) to rotate onto itself is given by:

\[ \frac{360°}{9} = 40° \]

Thus, the correct response is:

40°

Answer 4

Which of the following summarizes the reflections that carry a parallelogram onto itself?(1 point)
Responses

A parallelogram has two lines of reflection: flipped on each diagonal will carry it onto itself.
A parallelogram has two lines of reflection: flipped on each diagonal will carry it onto itself.

A parallelogram has four lines of symmetry: horizontal through the midpoints, vertical through the midpoints, and both diagonals.
A parallelogram has four lines of symmetry: horizontal through the midpoints, vertical through the midpoints, and both diagonals.

A parallelogram has two lines of reflection that carry it onto itself: one horizontal through the midpoints of each side, and one vertical through the midpoints of the top and bottom.
A parallelogram has two lines of reflection that carry it onto itself: one horizontal through the midpoints of each side, and one vertical through the midpoints of the top and bottom.

A parallelogram does not have any lines of reflection.

Answer 5

The response that best summarizes the reflections that carry a parallelogram onto itself is:

A parallelogram has two lines of reflection that carry it onto itself: one horizontal through the midpoints of each side, and one vertical through the midpoints of the top and bottom.

This statement is correct because a parallelogram has two lines of symmetry: one horizontal and one vertical that bisect the figure and allow it to map onto itself. The other option about diagonals is not accurate for general parallelograms since only rectangles and squares would have diagonals as lines of reflection.