Question

what is true about every rotation?
the angles in the image and pre-image are congruent
the image is smaller than the pre-image
the image is larger than the pre-image
the image overlaps the pre-image

Explanation:

1. Recall the properties of a rotation in geometry: A rotation is a rigid transformation, which means it preserves the shape and size of the figure.

• For the option "The image is smaller than the pre - image": Since rotation is a rigid transformation, the image and pre - image have the same size, so this is false.
• For the option "The image is larger than the pre - image": Again, because rotation preserves size, this is false.
• For the option "The image overlaps the pre - image": Not every rotation will result in the image overlapping the pre - image. For example, rotating a triangle 90 degrees about a point outside the triangle may not cause overlap.
• For the option "The angles in the image and pre - image are congruent": Since rotation preserves the shape (it's a rigid transformation), the corresponding angles of the image and pre - image are congruent.

Answer:

The angles in the image and pre - image are congruent