Organization of geometry

First, I have studied Geometry in the past.  I'm a software engineer.  I recently decided to review some advanced math concepts just for fun and to sharpen my mind a bit.  There is one thing that I found to be lacking in the foundations of geometry area, and that has to do with terminology.  It seems to me that Geometry is all about deductive reasoning, which means that the concepts of a postulates and theorems is a critical part of the foundation.  Some of the videos do a nice job of explaining things but not in terms of postulates and definitions that can serve as a foundation for proving theorems.  I think there should be more emphasis on terminology.  Knowing the difference between postulates and theorems is important as is the idea of being able to proof other things from that which we already know to be true.  Yet don't we need a point or reference?  To be able to prove that vertical angles are congruent, I first need to know the definition of lines and angles.  I guess I am just used to having points of references as numbers (i.e., postulate x states something), and then I refer to postulate x in a proof.  Right from the beginning a geometry student needs to know about terminology and the concept of having to prove things to be true.  When explaining fundamental concepts I would have thought that numbering them as Euclid did and stating them explicitly as postulates is necessary so that we can build upon that.  If we jump around looking at different types of objects (circles, squares, angles, triangles) we could learn to incorrectly prove things in a circular manner by assuming many things are already true.  Ultimately in Geometry don't we need to trace things back to the origins (postulates and axioms) in order to know for a fact that something is true?  I think the organization of the material is very confusing.  When something is stated to be fact, then it needs to be stated whether that is a constructive definition (A line is defined as such and such, or a circle is defined as such and such).  It's not always clear if the statements made by the teacher are definitions, postulates, axioms or what.