Final answer:
Side-Angle-Angle (SAA), also known as Angle-Side-Angle (ASA), is a valid criterion for triangle congruence when two angles and the included side are known, because the properties of triangles and the sum of their angles determine the remaining elements.
Step-by-step explanation:
The criterion of Side-Angle-Angle (SAA) is a valid means for establishing triangle congruence in specific circumstances. It's important to note that SAA is sometimes referred to as the Angle-Side-Angle (ASA) postulate, where the known angle is not sandwiched between the two known sides but rather one side is between the two known angles. According to the ASA postulate, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
To understand this, imagine we have two triangles with two angles and the side between them (the included side) matching in both triangles. Because the sum of angles in a triangle must always add up to 180 degrees, if two angles are known, the third is determined by subtracting the sum of the known angles from 180 degrees. Since the side lengths are the same, and the corresponding angles are equal, the triangles will overlap perfectly when superimposed, indicating that they are congruent. Triangulation is an application of this principle.