Segment Addition
Overview
When a point lies between two other points on the same line, the two smaller segments add up to the whole segment. That is the Segment Addition Postulate, and it turns pictures into equations: add the parts, set the sum equal to the whole, and solve. The key word is between — a point between two others is somewhere along the segment, not necessarily in the middle.
Vocabulary
- Between
- A point is between two other points when it is collinear with them and lies strictly between them on the segment joining them. Between does not mean in the middle.
- Segment Addition Postulate
- If point B is between points A and C, then AB + BC = AC.
- Collinear Points
- Points that lie on the same line. Betweenness requires collinearity: a point off the line cannot be between two points on it.
- Midpoint
- The point that divides a segment into two congruent segments. A midpoint is a special case of a point between two others — most points between are not midpoints.
Main Ideas
- Part + part = whole. Identify the two smaller segments and the full segment before writing anything.
- With plain numbers, add or subtract measures. With expressions, add the two part expressions and set the sum equal to the whole.
- Solve for x first, then substitute back — questions often ask for a segment's measure, not for x.
- Do not assume a point is a midpoint unless it is stated or marked. Avoid assumptions the picture does not support.
Lesson Notes
Flip through the notes one page at a time using the buttons below.
Lesson Video
Watch the lesson video.
Interactive Activity
Use the Segment Addition Postulate to build segment lengths — plus a challenge set with quadratic equations.
Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.