Given:
∠TRS = ∠URS
∠TSR = ∠USR
Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove the triangles congruent. If it is not possible to prove the triangles are congruent, choose "not possible
Based on the given information, the congruence theorem that could be used to prove the triangles congruent is the Angle-Angle (AA) Congruence Theorem. This theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are congruent.
Based on the given information, we can observe that two pairs of corresponding angles in the triangles are congruent. In order to prove the triangles congruent, we need to have a corresponding side-length relationship between the two triangles.
However, given only the angle congruence, it is not possible to determine the congruence theorem that could be used to prove the triangles congruent. The angle-angle-angle (AAA) congruence theorem requires all three pairs of corresponding angles to be congruent, not just two pairs.
Therefore, without additional information or corresponding side-length relationships, it is not possible to prove the triangles congruent.