Question

rotate triangle uvw counterclockwise about point w until uw has the same slope as pw. then reflect triangle uvw over uw.
answer attempt 1 out of 2
triangle uvw maps onto triangle pqw. this is possible because △uvw ≅ △pqw by dropdown with sas, asa, sss, aas, and one congruent figure can be mapped onto another using rigid motions.

Explanation:

Step1: Analyze the congruence criteria

We know that rigid motions (rotation and reflection in this case) preserve side - lengths and angles. When we rotate \(\triangle UVW\) about point \(W\) and then reflect it, we are looking at the congruence of two triangles.
Let's assume that \(UW = PW\) (from the rotation step where \(UW\) is mapped to \(PW\)), \(VW=QW\) (because of the congruence of the triangles after rigid motions), and \(\angle UWV=\angle PQW\) (angles are preserved in rigid motions).
The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer:

SAS