This is the "high school versiom" from Birkhoff and Beatley. B&B calls these Axioms Principles 1-5. There is another more sophisticated version published in a mathematics journal for mathematicians.
Important Note: These axioms are a combination of Principles 1-4 from B&B Chapter 2 with SAS from Chapter 1. B&B Princple 5 in Chapter 2 includes similarity. We will start with similarity late in Week 2.
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 equalt respectively to two sides and the included angle of the other, the two triangles are equal.