I want to know if there's a good book or any other type of guide to study Euclidean geometry by only the 5 axioms in plane geometry and prove every other theorems from them?


Of course, Euclid's Elements were written starting from those axioms. But we know now that Euclid did not use only those axioms. More precisely, he used other axioms implicitely. I suggest that you take a look at Robin Hartshone's Geometry: Euclid and Beyond or at David Hilbert's Foundations of Geometry.

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    $\begingroup$ The chapter Ordered Geometry in the book Introduction To Geometry, by Coxeter, is axiom-based. Euclid makes implicit assumptions about "betweenness"..... In elliptic geometry you can have three points on a line, all equidistant from each other, and it doesn't mean much to say whether any one of them is between the other two.......+1 $\endgroup$ – DanielWainfleet Nov 3 '18 at 20:02
  • $\begingroup$ Who is the author of Euclid's Elements? $\endgroup$ – Masked Man Nov 4 '18 at 9:31
  • $\begingroup$ I think that it's a safe bet to say that Euclid wrote Euclid's Elements. $\endgroup$ – José Carlos Santos Nov 4 '18 at 9:39
  • $\begingroup$ The other two book you offered match my criteria? $\endgroup$ – Masked Man Nov 4 '18 at 14:08
  • $\begingroup$ No, since the authors of both books know that other axioms are needed. $\endgroup$ – José Carlos Santos Nov 4 '18 at 14:09

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