a. Without a specific diagram or details regarding the positions of triangles ABC and XYZ, I can't identify the exact transformations used. However, a common example would involve a triangle being rotated and translated. For instance: "Triangle ABC was rotated by 90 degrees and then translated 5 units to the right."
b. To determine if the shapes are congruent, you would typically examine whether the corresponding sides and angles of triangles ABC and XYZ are equal. If all corresponding sides and angles are congruent, then the triangles are considered congruent. You could use the concept of transformations—like rotations, reflections, and translations—which preserve distance and angle measures, indicating that the shapes themselves have not changed during the transformations. If the transformations applied to triangle ABC can yield triangle XYZ without altering size or shape, then they are congruent.