Congruence of triangles: SSA criteria

Question

It is well known that this criteria does not work in general. I am trying to answer to the following question

if two triangles have two sides and the angle NOT between them equal, they are either congruent or..?

In other words, does it have a name when two triangles meet SSA but they are not equal?

Answer 1

Yes, it is either congruence or not. I can disprove $SSA$ congruence.

In $\triangle ABC $ and $\triangle DEF$,

let,$AB=DE$ , $BC=EF$ and $\angle BCA=\angle EFD$.

this condition does not say about $\angle B$ and $\angle E $ so, this condition does not work

see the visual disproof of $SSA$