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: Analyze dilation

Dilation is not a rigid transformation (it changes the size of the figure). Since \(\triangle ABC\cong\triangle FED\) (SSS congruence), we can rule out the option with dilation.

Step2: Analyze reflection - then - translation

If we first reflect \(\triangle ABC\) (to get the orientation similar to \(\triangle FED\) in terms of the right - angle position) and then translate (move the reflected triangle to the position of \(\triangle FED\)). Rigid transformations (reflection and translation) preserve the shape and size of the figure.

Step3: Analyze rotation - then - translation

Rotation changes the orientation of the figure. If we rotate \(\triangle ABC\), it is difficult to get the exact orientation of \(\triangle FED\) (with the right - angle in the position of \(E\) relative to \(F\) and \(D\)) and then translate it to map exactly onto \(\triangle FED\).

Step4: Analyze rotation - then - reflection

Combining rotation and reflection is more complex than the simple reflection - translation combination for mapping \(\triangle ABC\) onto \(\triangle FED\) as per their given positions.

Answer:

reflection, then translation