Question

the triangles are congruent by the sss congruence theorem. which rigid transformation(s) can map △abc onto △fed? reflection, then dilation reflection, then translation rotation, then translation rotation, then reflection

Explanation:

Step1: Recall rigid - transformation properties

Rigid transformations preserve shape and size. Dilation is not a rigid - transformation as it changes the size of a figure. So, the option with dilation is incorrect.

Step2: Analyze the orientation of the triangles

By observing the orientation of \(\triangle ABC\) and \(\triangle FED\), we can see that a rotation can be used to align the general direction of the triangles. Then, a translation can be used to map one triangle exactly onto the other. A reflection - then - translation would change the orientation in a way that is not consistent with the given congruent triangles. A rotation - then - reflection would also not map the triangles correctly.

Answer:

rotation, then translation