There are three main criteria for triangle congruence. If two triangles meet any one of these three criteria, they are considered congruent. ● Side-Side-Side [katex] (SSS) [/katex] criterion: Two triangles are congruent if all three of their corresponding side lengths are equal. ● Side-Angle-Side [katex] (SAS) [/katex] criterion: Two triangles are congruent if two of their corresponding side lengths and the angle between those sides are equal. ● Angle-Angle-Side [katex] (AAS) [/katex] criterion: Two triangles are congruent if two of their corresponding angles and the side between those angles are equal. In the case of right triangles, the Pythagorean theorem means that we can calculate the length of the third leg given the lengths of any other two. So right triangles are a special case of the Side-Side-Side criterion where we only need two pairs of congruent side lengths. ● Hypotenuse-Leg [katex] (HL) [/katex] criterion: Two right triangles are congruent if their hypotenuse lengths are equal and the lengths of one of their legs are equal. We don't need a Leg-Leg criterion for right triangles, because that would just be another case of Side-Angle-Side congruence.