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:

Step1: Analyze Reflection

First, check the reflection. The triangle \( \triangle ABC \) can be reflected over the line (like the perpendicular bisector or axis) to get a mirrored triangle (first transformation: reflection).

Step2: Analyze Rotation

After reflection, a rotation (around a point) would adjust the orientation to match the intermediate triangle.

Step3: Analyze Translation

Finally, a translation (shifting) would move the triangle to the position of \( \triangle A''B''C'' \). So the sequence is reflection, then rotation, then translation.

Answer:

D. reflection, then rotation, then translation