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 the orientation of the triangles

• $\triangle BCD$ and $\triangle WXY$ are not in the same orientation. A rotation alone cannot map $\triangle BCD$ onto $\triangle WXY$ because their relative positions are not just a rotational difference.
• A reflection alone also cannot map $\triangle BCD$ onto $\triangle WXY$ as their positions are not just a mirror - image without considering the shift.

Step2: Consider translation and then reflection

• First, translate $\triangle BCD$ (move it without rotation or reflection) so that one of its vertices (say \(C\)) is in a position relative to the other triangle.
• Then, reflect the translated $\triangle BCD$ over an appropriate line. For example, if we translate $\triangle BCD$ so that \(C\) is in a position corresponding to the side - length relationship and then reflect it, we can map it onto $\triangle WXY$.
• A translation - then - rotation combination won't work because the orientation change required is more of a reflection - type orientation change rather than a rotational one.

Answer:

translation, then reflection