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.