How to Use Segment Addition Postulate Calculator
The Segment Addition Postulate Calculator solves for the missing length when you know two of the three collinear segment lengths AB, BC, and AC. Select which length you want to find, enter the two known values, and the calculator returns the missing length with the full substitution shown. The Segment Addition Postulate Calculator runs entirely in your browser.
- Select what to solve for — Choose whether to find AC (the whole segment), AB (the first part), or BC (the second part).
- Enter the two known lengths — Type positive numbers for the two segment lengths you already know.
- Review the result — The Segment Addition Postulate Calculator shows the formula, the substituted values, and the computed missing length.
If a part is entered as longer than or equal to the whole, or if the computed result would be zero or negative, the calculator shows an error so you can correct the inputs.
Formula & Theory - Segment Addition Postulate Calculator
The Segment Addition Postulate Calculator is based on a fundamental geometry postulate:
If B is between A and C, then:
AB + BC = AC
Rearranged:
AB = AC − BC
BC = AC − AB| Variable | Meaning |
|---|---|
| A, C | Endpoints of the full segment |
| B | A point between A and C on the segment |
| AB | Distance from A to B |
| BC | Distance from B to C |
| AC | Total distance from A to C |
The postulate holds only when B is strictly between A and C. If B is at an endpoint, AB or BC becomes zero; if B is outside AC, the additive relationship no longer applies.
When the Postulate Applies
The Segment Addition Postulate Calculator assumes:
- All lengths are positive.
- The sum of the two parts equals the whole (no rounding gaps).
- B lies strictly between A and C on a straight line.
Use Cases for Segment Addition Postulate Calculator
The Segment Addition Postulate Calculator is a staple tool for geometry students and educators. Common uses include:
- Geometry homework — Quickly solve segment addition problems without manual arithmetic.
- Coordinate geometry — Verify that a midpoint or dividing point is correctly placed on a number line or line segment.
- Test preparation — Check answers to segment addition problems before submitting a test.
- Basic construction — Confirm that the measured partial lengths of a beam or path add up to the total.
By providing the formula, substitution, and computed result together, the Segment Addition Postulate Calculator helps students understand the reasoning behind each calculation, not just the answer.