Question

the diagram shows the sequence of three rigid transformations used to map △abc onto △abc. what is the sequence of the transformations? the triangles are congruent by sss or hl.

Explanation:

Step1: Analyze First Transformation

Looking at $\triangle ABC$ and $\triangle A'B'C'$, we can see that a rotation (around a point, likely $C$ or midpoint) aligns the sides. So first transformation: rotation.

Step2: Analyze Second Transformation

From $\triangle A'B'C'$ to the next triangle (before translation), a reflection over a vertical or horizontal line (to flip the triangle) occurs. So second transformation: reflection.

Step3: Analyze Third Transformation

From the reflected triangle to $\triangle A''B''C''$, a translation (shifting the triangle without rotation/reflection) moves it to the final position. So third transformation: translation.
So the sequence is rotation, then reflection, then translation.

Answer:

The option with "rotation, then reflection, then translation" (the third option in the vertical arrangement, or the left - middle option depending on layout; assuming the first column second row option as per typical diagram - option mapping here: the option with text "rotation, then reflection, then translation").