Question

the triangles shown are congruent by the sss congruence theorem. the diagram shows the sequence of three rigid transformations used to map △abc onto △abc. what is the sequence of the transformations? rotation, then reflection, then translation rotation, then translation, then reflection translation, then reflection, then rotation translation, then rotation, then reflection

Explanation:

Step1: Analyze the first transformation

First, observe the movement from \(\triangle ABC\) to \(\triangle A'B'C'\). The orientation of the triangle changes, which is characteristic of a rotation.

Step2: Analyze the second transformation

Next, from \(\triangle A'B'C'\) to the intermediate - step (before final mapping to \(\triangle A''B''C''\)), the triangle is flipped over a line (mirror - like change), which is a reflection.

Step3: Analyze the third transformation

Finally, from the intermediate - step (after reflection) to \(\triangle A''B''C''\), the triangle is shifted without rotation or reflection (all points move the same distance in the same direction), which is a translation.

Answer:

rotation, then reflection, then translation