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Why does one take SAS as an axiom for the neutral geometry and not AAS? Is there a model of "neutral geometry with SAS replaced by AAS" where SAS is false? Axioms for neutral geometry can be found in George E. Martin's "The Foundation of Geometry ad the Non-Euclidean Plane". (Essentially this question is posed in this textbook as an exercise)

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  • $\begingroup$ Do you have some particular axiomatization of neutral geometry in mind? I imagine this could depend on exactly what other axioms you have. $\endgroup$ – Eric Wofsey Dec 20 '17 at 5:27
  • $\begingroup$ @EricWofsey: "not an answer" deleted. : ) $\endgroup$ – zoli Dec 20 '17 at 7:25

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