1. The problem asks which rule explains why the two triangles TUV and XWY are congruent. 2. The Side-Angle-Side (SAS) congruence rule 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 triangles are congruent. 3. In the given triangles, side UV is equal to side XY (marked with red marks). 4. The angle at vertex U in triangle TUV is equal to the angle at vertex Y in triangle XWY (both marked with red angle marks). 5. The side adjacent to these angles, side TU in triangle TUV, corresponds to side XW in triangle XWY (also marked with red marks). 6. Since two sides and the included angle between them in triangle TUV are equal to the corresponding two sides and included angle in triangle XWY, the SAS rule applies. 7. Therefore, the triangles TUV and XWY are congruent by the SAS congruence rule. Final answer: The triangles are congruent by the Side-Angle-Side (SAS) rule.