Question

what are the characteristics of a rotation?
select all that apply.
a. the image and preimage are congruent.
b. the image and preimage are similar but not congruent.
c. lengths of segments are preserved.
d. measures of angles are preserved.

Explanation:

Step1: Recall properties of rotation

Rotation is a rigid transformation. Rigid transformations preserve shape and size. So, the pre - image and image are congruent. Congruent figures have equal corresponding side lengths (lengths of segments are preserved) and equal corresponding angle measures.

Step2: Analyze each option

• Option A: Since rotation is a rigid transformation, the image and pre - image are congruent.
• Option C: In a rotation (a rigid transformation), the lengths of corresponding segments in the pre - image and image are equal (preserved).
• Option D: In a rotation (a rigid transformation), the measures of corresponding angles in the pre - image and image are equal (preserved).
• Option B: Similar figures have the same shape but not necessarily the same size. Since rotation is a rigid transformation (preserves size), the image and pre - image are congruent (not just similar).

Answer:

A. The image and preimage are congruent.
C. Lengths of segments are preserved.
D. Measures of angles are preserved.