I'm wondering about the relationship between Eculid's work and modern high school geometry. In "two column proofs," certain reasons are considered acceptible for steps in the proof, such as those shown below, from here.
#16. Definition of alternate interior angles – says that “If two angles are alternate interior, then they are on opposite sides of a transversal and are both on the interior to two lines (whether parallel or not).”
#17. Alternate interior angle theorem – says that “If two lines are parallel and alternate interior angles are formed, then the angles will be congruent to one another.”
#18. Converse of alternate interior angle theorem – says that “If alternate interior angles are congruent, then the lines that form them will be parallel to one another.”
It strikes me that many of the reasons considered acceptable in these kinds of proof are similar to, but not identical to, postulates, definitions etc. given in Euclid.
What I'm wondering is if there is some kind of modern standard for these kinds of reasons, that captures the essence of Euclid's reasons, but which uses modern insights and concepts to make them more accessible.
By which I mean basically, is there some kind of canonical source for what counts as valid reasons for steps in modern high school geometry proofs, or is what we have a kind of collective cultural habit that is loosely based on Euclid's work but is not in anyway standardized?