Let us assume for the sake of argument that one had to teach plane Euclidean geometry to mature minds from another world who had never heard of it... Then the whole course might, I think, be tackled in two or three hours...one of them being occupied by the description of the axiom system, one by its useful consequences and possibly a third one by a few mildly interesting exercises.
Everything else which now fills volumes of “elementary geometry”...and by that I mean, for instance, everything about triangles (it is perfectly feasible and desirable to describe the whole theory without even defining a triangle!) almost everything about inversion, systems of circles, conics, etc.,...has just as much relevance to what mathematicians (pure and applied) are doing today as magic squares or chess problems! 
KeywordsMathematics Teacher Euclidean Geometry Axiom System High School Teacher Geometric Intuition
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