Question

what are the characteristics of a translation?
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 the properties of translation

Translation is a rigid transformation. Rigid transformations preserve the shape and size of the figure.

Step2: Analyze each option

• Option A: In translation, the image and pre - image are congruent (since size and shape are preserved). So, this option is incorrect as it says "not congruent".
• Option B: Translation is a rigid transformation (preserves size and shape), so the image and pre - image are congruent (not just similar). Similarity allows for a change in size, but translation does not. So, this option is incorrect.
• Option C: In translation, the lengths of segments are preserved. Because it is a rigid transformation (distance between any two points in the pre - image and the image is the same).
• Option D: In translation, the measures of angles are preserved. Since it is a rigid transformation (angle - measure is a property that is invariant under translation).

Answer:

C. Lengths of segments are preserved. D. Measures of angles are preserved.