what are the rigid transformations that will map △abc to △def? translate vertex a to vertex d, and then…

what are the rigid transformations that will map △abc to △def? translate vertex a to vertex d, and then reflect △abc across the line containing ac. translate vertex b to vertex d, and then rotate △abc around point b to align the sides and angles. translate vertex b to vertex d, and then reflect △abc across the line containing ac. translate vertex a to vertex d, and then rotate △abc around point a to align the sides and angles.

what are the rigid transformations that will map △abc to △def? translate vertex a to vertex d, and then reflect △abc across the line containing ac. translate vertex b to vertex d, and then rotate △abc around point b to align the sides and angles. translate vertex b to vertex d, and then reflect △abc across the line containing ac. translate vertex a to vertex d, and then rotate △abc around point a to align the sides and angles.

Answer

Explanation:

Step1: Analyze translation

First, we need to match one - to - one corresponding vertices. Translating vertex A to vertex D is a valid first step as it starts to align the two triangles.

Step2: Analyze rotation

After translating vertex A to vertex D, rotating △ABC around point A can align the sides and angles of △ABC and △DEF. Other options have incorrect combinations of transformations. For example, reflecting across the line containing AC in the first and third options won't align the triangles correctly, and rotating around point B in the second option is wrong as we should start with aligning a corresponding vertex first.

Answer:

Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.