Question

Destiny wants to know if a quadrilateral can be rotated so that each side is parallel to the corresponding side of its image.

Which statement is true?
A) This is possible only for 180° rotations.

B) This is possible for all types of rotations.

C) This is possible for any clockwise rotation.

D) This is not possible for any type of rotation.

Answer 1

A) Only for 180° rotations

Explanation:

You want to know if a quadrilateral can be rotated so that each side is parallel to the corresponding side of its image.

Rotation

In general, a line segment's image will be parallel to the original if it is rotated 180°. Hence the line segments that make up a quadrilateral's image will be parallel to corresponding sides if the quadrilateral is rotated 180°.

The attachment shows a quadrilateral rotated 180°.

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Additional comment

We assume that the "corresponding side" of AB is A'B' in the image.

If square ABCD is rotated 90°, then side AB will be parallel to side B'C', and the same will be true for 3 other pairs of sides. For the purpose of this question, we don't consider AB and B'C' to be "corresponding" sides.