Question

select the correct answer.
a parallelogram rotates about its center. at what angle of rotation will the image of the parallelogram coincide with its preimage?
a. 30°
b. 90°
c. 180°
d. 270°
e. 315°

Explanation:

Step1: Recall properties of parallelograms

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

Step2: Determine the angle of rotational symmetry

For a parallelogram, when rotated about its center by \(180^\circ\), the image coincides with the pre - image. This is because the opposite sides and angles of a parallelogram are equal, and a \(180^\circ\) rotation swaps the positions of the vertices in a way that the figure maps onto itself. Rotations of \(30^\circ\), \(90^\circ\), \(270^\circ\), and \(315^\circ\) do not map a general parallelogram onto itself.

Answer:

C. \(180^\circ\)