These triangles have at most one congruent pair of sides. This means that two pairs of sides are not congruent. Since congruent triangles have congruent corresponding parts, these two triangles cannot be congruent.
In the figure, we see that the triangles have two corresponding congruent sides. Let's find the measure of the missing angle of the triangle at the right using the Triangle Angle Sum Theorem. The above means that the triangles have two congruent corresponding sides and an included congruent pair of angles. Therefore, by the Side-Angle-Side Congruence Theorem, the triangles are congruent.