Axioms as agreed in the book "Math Proofs Demystified"

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I am reading this book "Math Proofs Demystified" by Stan Gibilisco in which the author treats all of the congruence criteria/theorems of triangles as axioms instead of treating of one of them as axioms as using it to prove others as theorems, not only that he also defines sum, difference n product of fractions as axioms. Is this justified ?