Question

select all the sequences of transformations that always maintain congruence. a a reflection and then a translation b a translation and then a rotation c a dilation and then a reflection d a translation and then a dilation e a rotation and then a dilation f a rotation and then a reflection

Explanation:

Step1: Recall congruence - preserving transformations

Rigid - motions (translations, rotations, and reflections) preserve congruence. Dilations change the size of a figure and do not preserve congruence.

Step2: Analyze each option

• Option A: A reflection and then a translation are both rigid - motions. They preserve congruence.
• Option B: A translation and then a rotation are both rigid - motions. They preserve congruence.
• Option C: A dilation changes the size, so a dilation and then a reflection do not always maintain congruence.
• Option D: A translation is a rigid - motion, but a dilation changes size. So a translation and then a dilation do not always maintain congruence.
• Option E: A rotation is a rigid - motion, but a dilation changes size. So a rotation and then a dilation do not always maintain congruence.
• Option F: A rotation and a reflection are both rigid - motions. They preserve congruence.

Answer:

A. a reflection and then a translation
B. a translation and then a rotation
F. a rotation and then a reflection