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We were studying demonstrative geometry, so I thought if I read Euclid's Elements it would give me the proper conceptual basis to understand the theorems. But then I learned that Euclid's method of proving congruence is not accepted today and many of his propositions have no axioms to support them; so I am left where I started.

I want to read a good book that teaches the basics of Euclidean geometry pretty much like Euclid's Elements but does not use analysis or advanced mathematical methods, just simple geometrical theorems. Also, it should be rigorous and consistent with today's standards.

Some people might recognize this as a duplicate so let me just add one more thing; it should be able to be understood by any student with secondary level education. Euclid's Elements may not be rigorous but I was still able to understand it easily.

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  • $\begingroup$ Possible duplicate of math.stackexchange.com/questions/107882/…. $\endgroup$ – lhf Jul 30 '15 at 12:37
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    $\begingroup$ I would suggest not to be quite so quick to dismiss Euclid. Yes, he leaves certain principles unstated: axioms, or postulates, or definitions. But understanding his proofs, which are otherwise rock solid, is an excellent way to understand, in conjunction with other readings, just what Euclid missed. $\endgroup$ – Lee Mosher Jul 30 '15 at 12:40
  • $\begingroup$ @lhf I added a little at the end. I hope you will forgive me. ; ) $\endgroup$ – Abdur Rahman Jul 30 '15 at 12:43
  • $\begingroup$ @LeeMosher I am not dismissing Euclid. His book is still universal, but the problem is I want to know proofs to simple postulates as the SAS in way I can understand. I am sure there must be some good books on basic geometry. $\endgroup$ – Abdur Rahman Jul 30 '15 at 12:46
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refer to Robin hartsthorne: Geometry, Euclid and Beyond. No need to endorse this book!

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  • $\begingroup$ Could you also provide a PDF link? $\endgroup$ – Abdur Rahman Jul 30 '15 at 13:17

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