This is the "informal" version of the axioms as found in a high school text Basic Geometry by Birkhoff and Beatley (abbreviated B&B). In that text these Axioms are called Principles 1-5. There is another more sophisticated version published in a mathematics journal for mathematicians.
The points on any straight line can be numbered so that number differences measure distances.
There is one and only one straight line through two given points.
At this point, some definitions are made, including the definition of a half-line and straight angle.
All half-lines having the same endpoint can be numbered so that number differences measure angles.
All straight angles have the same measure.
At this point, some definitions are made, including the ones used in the final Axiom.
If in two triangles, two sides and the included angle of one are congruent respectively to two sides and the included angle of the other, the two triangles are congruent.
Important Note: B&B Principle 5 in Chapter 2 states SAS for similarity. We will start with the congruence version and develop similarity from the Parallel Postulate, as explained later.