Question

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

Explanation:

Step1: Analyze the orientation of the triangles

Triangle \( \triangle BCD \) and \( \triangle WXY \) have different orientations. A single rotation or translation cannot map \( \triangle BCD \) onto \( \triangle WXY \).

Step2: Consider the effect of translation and reflection

A translation moves \( \triangle BCD \) to the general position of \( \triangle WXY \), and then a reflection (which changes the orientation) can map \( \triangle BCD \) exactly onto \( \triangle WXY \). A translation - then - rotation would not correct the orientation as needed (since rotation and translation are both orientation - preserving in 2D Euclidean geometry when rotation is by an angle that is a multiple of \( 360^{\circ}/n,n\in\mathbb{Z} \), and here the orientation change is a non - rotational orientation change). A single reflection or rotation cannot account for the position and orientation change from \( \triangle BCD \) to \( \triangle WXY \) as required by their congruence (based on the SSS theorem, we know they are congruent, and we need to find the transformation).

Answer:

translation, then reflection