If B lies on line AC and points A, B, and C are distinct such that, AB + BC = AC, then: 

By using ruler postulates the points on a line can be arranged in such a way that: there is a one-to-one correspondence between the set of points on the line and the set of real numbers, and the distance between two points equals the absolute value of the difference of the corresponding numbers.

To understand this better, let's mark two points A and C, and join both points with a straight line. We get a line segment AC.

On this line segment AC let's mark point B. Since A, B, and C are distinct points on AC, we have line segments AB and BC which together make line segment AC. 

AC - AB = BC or AC - BC = AB

Since point B lies on line AC, then AB must be shorter than AC  i.e., AB < AC.