There is no AAA theorem since it is not true.
SSS is, in fact a theorem, not a postulate. It states that if the three sides of one triangle are equal in magnitude to the corresponding three sides of another triangle, then the two triangles are congruent.
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Well, this will depend on the length of the sides of the triangle for what postulate or theorem you will be using.
The first thing you prove about congruent triangles are triangles that have same side lines (SSS) is congruent. (some people DEFINE congruent that way). You just need to show AAS is equivalent or implies SSS and you are done. That's the first theorem I thought of, don't know if it works though, not a geometry major.
SAS
Two congruent triangles.. To prove it, use the SSS Postulate.
No. SSA can give rise to a pair of non-congruent triangles.