Question

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

Explanation:

Step1: Analyze the orientation change

First, we observe that the orientation of the triangle changes. A rotation is needed to change the orientation of $\triangle ABC$ to match the intermediate - stage triangle.

Step2: Analyze the position change

After rotation, the position of the triangle needs to be adjusted to exactly match $\triangle A''B''C''$. A translation is required to move the rotated triangle to the final position.

Step3: Analyze the reflection need

There is no indication of a reflection as the orientation and side - to - side correspondence can be achieved without flipping the triangle over a line.

Answer:

rotation, then translation