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? rotation, then reflection, then translation rotation, then translation, then reflection reflection, then translation, then rotation reflection, then rotation, then translation

Explanation:

• First, observe the orientation change from \(\triangle ABC\) to \(\triangle A'B'C'\). A rotation (around a point, say \(C\)) can change the orientation of \(\triangle ABC\) to get a new - shaped triangle (similar to the intermediate - step triangle).
• Then, a reflection (over a line, which can flip the triangle to get a mirror - image - like shape relative to the rotated triangle).
• Finally, a translation (moving the triangle without rotation or reflection) to map it exactly onto \(\triangle A''B''C''\).

Answer:

rotation, then reflection, then translation