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. Dilation is not a rigid - transformation as it changes the size of the figure. Since \(\triangle ABC\) and \(\triangle FED\) are congruent, we need to use only rigid - transformations to map one onto the other.

Step2: Analyze each option

A dilation would change the size of \(\triangle ABC\), so we can eliminate the option with dilation. A rotation and then a translation can map \(\triangle ABC\) onto \(\triangle FED\). A rotation first changes the orientation of \(\triangle ABC\) and then a translation moves it to the position of \(\triangle FED\).

Answer:

rotation, then translation