Since the triangles are congruent, there is a sequence of one or more rigid motions that maps one figure onto the other. Translations, rotations, and reflections are all congruence transformations. Let's consider the given diagram.
It appears that △ XYZ is the image of △ LMN after a rotation 270^(∘) about the origin, followed by a reflection across the x-axis. Let's confirm whether this is true.
We can see that R_(x-axis) ∘ r_((270^(∘),O)) ( △ LMN)= △ XYZ. Therefore, R_(x-axis) ∘ r_((270^(∘),O)) is a congruence transformation that maps △ LMN to △ XYZ.
