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, analyze the initial position of \( \triangle ABC \) and the intermediate steps. A translation would move the triangle without rotating or reflecting. Then, a rotation would change the orientation around a point. Finally, a reflection (over a line) would flip the triangle to match \( \triangle A''B''C'' \).
2. Check the other options:

• Rotation first would not align the triangle's position initially as well as translation.
• The order of rotation then reflection then translation or other incorrect orders don't match the rigid transformation sequence needed to map \( \triangle ABC \) to \( \triangle A''B''C'' \).
• The correct sequence is translation (to move the triangle closer), then rotation (to adjust orientation), then reflection (to flip and match the final position).

Answer:

D. translation, then rotation, then reflection