Final Answer:
If t is the midpoint of su¯¯¯¯¯ and rv¯¯¯¯¯, the triangle congruence statement that can be used to prove rs¯¯¯¯¯≅uv¯¯¯¯¯ is SAS (Side-Angle-Side).
Step-by-step explanation:
In geometry, when proving triangle congruence, SAS (Side-Angle-Side) is a valid criterion. In this scenario, since t is the midpoint of su¯¯¯¯¯ and rv¯¯¯¯¯, we can establish that the segments st¯¯¯¯¯ and tv¯¯¯¯¯ are congruent due to the definition of a midpoint.
Additionally, the shared side tu¯¯¯¯¯ is common to both triangles, providing the side-angle-side configuration. This implies that the two triangles, rst¯¯¯¯¯ and tuv¯¯¯¯¯, are congruent by SAS.
The congruence of these triangles allows us to conclude that rs¯¯¯¯¯≅uv¯¯¯¯¯, as corresponding sides of congruent triangles are equal. Therefore, the application of the SAS congruence statement is appropriate in this context, demonstrating the equality of rs¯¯¯¯¯ and uv¯¯¯¯¯.