select the correct answer.\na parallelogram rotates about its center. at what angle of rotation will the…

select the correct answer.\na parallelogram rotates about its center. at what angle of rotation will the image of the parallelogram coincide with its preimage?\na. 30°\nb. 90°\nc. 180°\nd. 270°\ne. 315°

select the correct answer.\na parallelogram rotates about its center. at what angle of rotation will the image of the parallelogram coincide with its preimage?\na. 30°\nb. 90°\nc. 180°\nd. 270°\ne. 315°

Answer

Explanation:

Step1: Recall properties of parallelograms

A parallelogram has rotational symmetry. The center of rotation is the intersection of its diagonals.

Step2: Determine the angle of rotation

For a general parallelogram (non - square, non - rectangle with more symmetry), the smallest angle by which it can be rotated about its center to coincide with its pre - image is (180^{\circ}). Rotating a parallelogram by (180^{\circ}) about its center maps each vertex to the opposite vertex, and the sides will align with the original sides. Angles like (30^{\circ}), (90^{\circ}), and (270^{\circ}) do not map the parallelogram onto itself.

Answer:

C. (180^{\circ})