No. SSA can give rise to a pair of non-congruent triangles.
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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.
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.
SAS
Theorem: A Proven Statement. Postulate: An Accepted Statement without Proof. They mean similar things. A postulate is an unproven statement that is considered to be true; however a theorem is simply a statement that may be true or false, but only considered to be true if it has been proven.
Personality is subjective and so cannot be proven. However, it should not be accepted without challenge either.