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 include rotation, reflection, and translation and preserve the shape and size of a figure. Dilation is not a rigid - transformation as it changes the size of the figure.

Step2: Analyze the options

We want to map $\triangle ABC$ onto $\triangle FED$. Since the two triangles are congruent (by SSS congruence), we can use a combination of rigid - transformations. A rotation can be used to re - orient $\triangle ABC$ and then a translation can be used to move it to the position of $\triangle FED$.

Answer:

rotation, then translation