Question

the triangles are congruent by the sss congruence theorem
which transformation(s) can map △bcd onto △
wxy?
rotation only
reflection only
translation, then rotation
translation, then reflection

Explanation:

Step1: Analyze transformation types

Rotation only would not align the triangles as their orientations and positions are not just a rotation apart. Reflection only also won't work as their positions are not just a mirror - image across a line without re - positioning.

Step2: Consider translation and reflection

First, translate \(\triangle BCD\) so that one of its vertices (say \(C\)) is in a position relative to \(\triangle WXY\) (similar to the congruent side - side - side structure). Then, a reflection can be used to map the translated \(\triangle BCD\) onto \(\triangle WXY\) because after translation, the orientation (which is different initially) can be corrected by reflection to match the congruent triangle \(\triangle WXY\) (since they are congruent by SSS, their side lengths are equal, and after translation and reflection, the vertices and sides will coincide).
Translation then rotation won't work as rotation (after translation) won't correct the orientation in the same way as reflection does for the given congruent triangle pair.

Answer:

translation, then reflection