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:

1. First, recall rigid transformations: reflection, rotation, translation (dilation is non - rigid as it changes size, so eliminate option with dilation).
2. Analyze the orientation of \(\triangle ABC\) and \(\triangle FED\). \(\triangle ABC\) has a right angle at \(B\), \(\triangle FED\) has a right angle at \(E\). A reflection can flip the triangle to match the orientation, and then a translation can move it to the position of \(\triangle FED\). Rotation followed by reflection or rotation followed by translation do not match the orientation and position change as well as reflection then translation.

Answer:

B. reflection, then translation