SSS stands for "side, side, side." If two triangles have three corresponding congruent sides, the triangles are congruent. If you know that all 3 pairs of corresponding sides in two triangles are congruent, you don't need to know anything about the angles. Here's an example of how to use the SSS property to show congruence.

For triangles ABC and XWY we know \(\small\mathsf{ \overline{AB} }\) ≅ \(\small\mathsf{ \overline{XW} }\), \(\small\mathsf{ \overline{AC} }\) ≅ \(\small\mathsf{ \overline{XY} }\) and \(\small\mathsf{ \overline{BC} }\) ≅ \(\small\mathsf{ \overline{WY} }\), so these two triangles are congruent by SSS congruence.

SAS stands for "side, angle, side." If two triangles have two pairs of corresponding congruent sides plus congruent included angles, then the two triangles are congruent. An included angle is the angle that is formed by the intersection of the two sides. Here's an example of SAS congruence.

For triangles DCE and ORN we know \(\small\mathsf{ \overline{DC} }\) ≅ \(\small\mathsf{ \overline{OR} }\), \(\small\mathsf{ \overline{CE} }\) ≅ \(\small\mathsf{ \overline{RN} }\) and the included angles,  \(\mathsf{ \angle }\)C and \(\mathsf{ \angle }\)R, are congruent. Notice that the angles are formed by two sides, therefore they are included angles.

ASA stands for "angle, side, angle." If two triangles have two pairs of corresponding congruent angles plus one pair of included corresponding congruent sides, the two triangles are congruent. This congruent side is called an included side because it is shared by the two congruent angles. The following is an example of ASA congruence.

For triangles OBW and AMN we know \(\mathsf{ \angle }\)B ≅ \(\mathsf{ \angle }\)M, \(\mathsf{ \angle }\)O ≅ \(\mathsf{ \angle }\)A, and included sides \(\small\mathsf{ \overline{BO} }\) and \(\small\mathsf{ \overline{MA} }\) are also congruent.