Question

determine which triangle congruence theorem explains how the triangles are congruent.

side - side - side congruence theorem

angle - angle - side congruence theorem

side - angle - side congruence theorem

angle - side - angle congruence theorem

Explanation:

The Angle - Angle - Side (AAS) Congruence Theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
In the given figure, we have two angles (the blue angles at \(R\) and the red angles at \(E\) and \(V\)) and a non - included side (the side marked with three lines in the middle).

Answer:

Angle - Angle - Side Congruence Theorem