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There are some cases when SSA can imply triangle congruence, but not always. This is why it's not like the other triangle congruence postulates/criteria.
Proving the SAS triangle congruence criterion using transformations (Opens a modal) Proving the ASA and AAS triangle congruence criteria using transformations
Sal explains what it means for triangles to be congruent and what is a postulate/axiom. He also presents the SSS congruence postulate/criterion and its justification.