We can use SSS, ASA, AAS, SAS, and HL to prove triangle congruence, but why do AAA and SSA not work to prove triangles congruent? Write your best guess below.
AAA (Angle-Angle-Angle) does not work to prove triangle congruence because two triangles can have the same three angles but still have different side lengths and therefore be different shapes.
SSA (Side-Side-Angle) also does not work to prove triangle congruence because two triangles can have the same side-lengths and one congruent angle, but still be different shapes. The angle given could be an acute angle or a obtuse angle, resulting in the possibility of two different solutions and therefore not being a sufficient condition for congruence. Additionally, if the given angle is a right angle, it could be the hypotenuse of a right triangle and have infinitely many possible side lengths, leading to different shapes as well.