The SAS (Side-Angle-Side) criterion can be used to prove the similarity of two triangles as follows:
If two corresponding side lengths of each triangle are given and proportional, with a proven included angle measure, then the triangles are similar. This means that if you have two sides of one triangle in proportion to the two sides of another triangle, and the angles included between those pairs of sides are equal, the triangles can be considered similar.
For example, if triangle ABC has sides AB and AC proportional to sides DE and DF of triangle DEF (i.e., AB/DE = AC/DF), and the included angle ∠BAC is equal to ∠EDF, then triangles ABC and DEF are similar by the SAS criterion.
This similarity implies that the corresponding angles are equal and the lengths of the corresponding sides are in proportion, thus forming a consistent scale factor.