Question

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

Explanation:

Step1: Analyze the first transformation

First, observe that \(\triangle ABC\) to \(\triangle A'B'C'\) is a reflection. Reflection flips a figure over a line.

Step2: Analyze the second transformation

Then, from \(\triangle A'B'C'\) to the intermediate - step (before final mapping to \(\triangle A''B''C''\)), we note that a rotation is not the next step. The orientation of the triangle relative to the axes (if we assume a coordinate - like mental model) changes in a non - rotational, non - reflectional way that is characteristic of translation for the second step. Translation slides a figure without rotating or reflecting it.

Step3: Analyze the third transformation

Finally, from the translated triangle (after the second step) to \(\triangle A''B''C''\), we see a rotation. Rotation turns a figure around a point.

Answer:

reflection, then translation, then rotation