The simple answer is that these two methods don't always work. Side-Side-Angle [katex] (SSA) [/katex] seems like it could work, but it's possible to have two triangles with the same angle and two side measurements that aren't congruent. The same goes for Angle-Angle-Angle [katex] (AAA). [/katex] Two triangles can have the same three angles but not be congruent. This is why we use the four methods that do work: Side-Side-Side [katex] (SSS), [/katex] Side-Angle-Side [katex] (SAS), [/katex] Angle-Side-Angle [katex] (ASA), [/katex] and Hypotenuse-Leg [katex] (HL) [/katex] for right triangles. These methods have been proven to work every time, so we can rely on them to show that two triangles are congruent.