Axiom  Manipulative  Discussion 
II,1 
 Manipulative 1: Axiom of order II,1. Click on the blue points in the manipulative to change the figure. 

"If A, B, and C are points of a straight line and B lies between A and C, then B lies
also between C and A."^{[2]}
This tells us that if point B is between A and C, then it is also between points C and A.

II,2 
 Manipulative 2: Axiom of order II,2. Created with GeoGebra. 

"If A and C are two points of a straight line, then there exists at least one point B
lying between A and C and at least one point D so situated that C lies between A and
D."^{[2]}
This axiom establishes that between any two points on a line, there exists another point. A
consequence of this axiom is that an
infinite
number of points lie between any two points on a line.

II,3 
 Manipulative 3: Axiom of order II,3. Created with GeoGebra. 

"Of any three points situated on a straight line, there is always one and only one
that lies between the other two."^{[2]}
This says that if point B lies between points A and C then point
A can not lie between points B and C.

II,4 
 Manipulative 4: Axiom of order II,4. Created with GeoGebra. 

"Any four points A, B, C, D of a straight line can always be arranged so that B
shall lie between A and C and also between A and D, and, furthermore, that C shall lie between
A and D and also between B and D."^{[2]}
This axiom establishes that point on a line can always be put in order.

II,5 
 Manipulative 5: Axiom of order II,5. Created with GeoGebra. 

"Let A, B, C be points not lying in the same straight line and let a be a
straight line lying in the plane ABC and not passing through any of the points A, B, C.
Then, if a straight line passes through a point of segment AB, it will always pass through
either a point of the segment BC or a point of the segment
AC."^{[2]}
This axiom establishes that a straight line that intersects one side of a triangle, must
also intersect a second side of the same triangle.
