Question

Given: ∠T = ∠U ∠TRS = ∠URS 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".
SSS
SAS
AAS
not possible

Answer 1

AAS. It would be this because there are 2 angles and one side, and that is the only option with 2 angles and 1 side. The side is not included in the two angles.

Answer 2

Two triangles are congruent, if there is isometry, which one triangle maps into another, that is, they are congruent, if they have the equal corresponding elements, sides and angles. In order to prove congruence, it is not necessary to know all the elements of these triangles. There are sufficient conditions for congruence, which are given through four rules for the congruence. In this case, we have one side that is equal and two angles that are equal, but it is necessary that both angles that are equal are placed on a side that is equal. Here we have only one angle that is placed on the equal side, while the other is opposite to it. However, in this specific setting, we can conclude that the triangles are congruent based on AAS.