Question

the triangles shown are congruent by the sss congruence theorem.
the diagram shows the sequence of three rigid transformations used to map $\triangle abc$ onto $\triangle abc$. what is the sequence of the transformations?
\bigcirc rotation, then reflection, then translation
\bigcirc rotation, then translation, then reflection
\bigcirc translation, then reflection, then rotation
\bigcirc translation, then rotation, then reflection

Explanation:

1. First, observe $\triangle ABC$ is shifted to the position of $\triangle A'B'C'$; this is a translation (sliding without rotating/flipping).
2. Next, $\triangle A'B'C'$ is flipped over a line to match the orientation of the intermediate triangle; this is a reflection.
3. Finally, the reflected triangle is turned to map onto $\triangle A''B''C''$; this is a rotation.

Answer:

translation, then reflection, then rotation