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.

Answer 1

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.