1. **Stating the problem:** We want to understand the rule that states for points A, B, and C on a line, the length from A to B plus the length from B to C equals the length from A to C. 2. **The rule:** This is called the Segment Addition Postulate. It says: $$AB + BC = AC$$ where $AB$, $BC$, and $AC$ are the lengths of the segments between points A, B, and C. 3. **Explanation:** If point B lies between points A and C on a straight line, then the distance from A to C is the sum of the distances from A to B and from B to C. 4. **Example:** Given $AB = 8$, $BC = 3$, then: $$AB + BC = 8 + 3 = 11$$ If $AC$ is also 11, then the rule holds. 5. **Checking the example in the problem:** The user wrote $8 + 3 \neq 10$, which means $AB + BC \neq AC$ if $AC = 10$. This shows that points A, B, and C are not collinear in that case or the lengths are inconsistent. 6. **Summary:** The Segment Addition Postulate only applies when B is between A and C on a straight line, and the lengths must satisfy $AB + BC = AC$ exactly. This rule helps us find missing segment lengths or verify if points lie on a line segment correctly.