The segment addition postulate is one of the basic axioms of geometry: parts of a segment add up to the whole. It is used to set up equations like “AB = 2x + 3, BC = x − 1, AC = 20”.
How to use the Segment Addition Postulate Calculator
- Find
- AB
- BC
- AC
Results update as you type, and everything is calculated in your browser.
How it works
Choose which segment is unknown and enter the other two. The result must be positive; otherwise B cannot lie between A and C.
Inputs explained
| Field | What to enter |
|---|---|
| Find | Choose one: AC (whole segment), AB, BC |
| AB | Units: cm, m, mm, in, ft, yd … |
| BC | Units: cm, m, mm, in, ft, yd … |
| AC | Units: cm, m, mm, in, ft, yd … |
Example values
How the main result changes when AB changes and everything else stays at the example values above:
| AB (cm) | Missing segment (cm) |
|---|---|
| 2 | 8 |
| 3 | 9 |
| 4 | 10 |
| 5 | 11 |
| 6 | 12 |
| 8 | 14 |
Formula
AB + BC = AC (B lies between A and C)
Worked example
Inputs — Find: AC (whole segment); AB: 4 cm; BC: 6 cm.
Results — Missing segment = 10 cm; Ratio AB : BC = 0.666667.
Key terms
- Collinear
- Lying on the same straight line.
Frequently asked questions
What is a postulate?
A statement accepted without proof as a starting point.
What if B is not between A and C?
Then AB + BC ≠ AC; the formula does not apply.
How do I solve with algebra?
Substitute the expressions into AB + BC = AC and solve for x.
Is there an angle version?
Yes – the angle addition postulate.