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 Rigid Transformations

Rigid transformations preserve shape and size (reflection, rotation, translation; dilation is non - rigid). So we can eliminate the option with dilation (reflection, then dilation).

Step2: Compare Triangle Orientations

$\triangle ABC$ and $\triangle FED$: First, we can rotate $\triangle ABC$ to align the right angles and corresponding sides, then reflect (or vice - versa) to match the orientation. Let's check the options:

• Option "reflection, then translation": The orientation difference is better handled with rotation first in this case.
• Option "rotation, then translation": Translation alone after rotation may not align the triangles correctly.
• Option "rotation, then reflection": Rotating $\triangle ABC$ to get the right angle and side lengths in a position closer to $\triangle FED$, then reflecting to match the orientation (since the triangles are congruent right triangles with a flip in orientation that can be fixed by reflection after rotation) fits.
• The first option is out as dilation is non - rigid.

Answer:

rotation, then reflection