The phrase "other differences" implies that you already have some differences in mind. However, you have not bothered to share that information. Consequently, there is no way for me to know if a difference that I mention is one that you already know or if it is another one.
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When a postulate has been proven it becomes a theorem.
theorem
There is nothing true about the AAA theorem and the SSS postulate because the AAA postulate is not true!
a theorem that follows directly from another theorem or postulate, with little of no proof
converse of the corresponding angles postulate