Question

the triangles are congruent by sss or hl.
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 reflection, then translation, then rotation
\bigcirc reflection, then rotation, then translation

Explanation:

1. First, analyze the initial transformation from \( \triangle ABC \) to the intermediate triangle (before the last one). A reflection over the line \( BC \) (or the vertical line through \( C \)) would flip \( \triangle ABC \) to get a triangle with \( A' \), matching the first intermediate step.
2. Then, a rotation: rotating the reflected triangle around a point (like \( C' \) or another vertex) to align the sides better.
3. Finally, a translation: moving the rotated triangle to map onto \( \triangle A''B''C'' \) by shifting it horizontally/vertically. So the sequence is reflection, then rotation, then translation.

Answer:

D. reflection, then rotation, then translation