📏 Segment Addition Postulate Calculator
Calculate segment lengths using the segment addition postulate
Note: Assuming points A, B, C are collinear with B between A and C.
How to Use This Calculator
Choose Calculation Type
Select whether you want to find AC from three collinear points, or find BC from known AC and AB lengths.
Enter Values
Input the required values based on your selected calculation type (coordinates or segment lengths).
Click Calculate
Press the "Calculate" button to apply the segment addition postulate and get segment lengths.
Formula
AC = AB + BC
If point B lies on segment AC, then AC = AB + BC
Segment Addition Postulate:
If point B is between points A and C on a line segment, then AB + BC = AC.
Example: If A = 0, B = 5, C = 12 on a number line:
AB = |5 - 0| = 5
BC = |12 - 5| = 7
AC = AB + BC = 5 + 7 = 12
Example 2: If AC = 20 and AB = 8:
BC = AC - AB = 20 - 8 = 12
About Segment Addition Postulate Calculator
The Segment Addition Postulate Calculator helps you apply the segment addition postulate to find unknown segment lengths. The postulate states: If point B is between points A and C, then AB + BC = AC.
When to Use This Calculator
- Geometry: Solve segment length problems in geometry
- Education: Learn and practice the segment addition postulate
- Construction: Calculate segment lengths in construction and design
- Engineering: Find component lengths in linear systems
- Surveying: Calculate distances along straight paths
- Coordinate Geometry: Work with collinear points and segments
Why Use Our Calculator?
- ✅ Two Methods: Calculate from coordinates or direct lengths
- ✅ Instant Results: Get segment lengths immediately
- ✅ Step-by-Step Display: See the calculation formula
- ✅ Educational: Learn the segment addition postulate
- ✅ 100% Accurate: Precise geometric calculations
- ✅ Completely Free: No registration required
Understanding Segment Addition Postulate
The Segment Addition Postulate is a fundamental concept in geometry:
- Definition: If point B is between points A and C, then AB + BC = AC
- Collinearity: All three points must lie on the same line
- Betweenness: Point B must be between A and C (not just collinear)
- Additive Property: Segment lengths add together when points are collinear and in order
- Fundamental: This is a basic postulate used throughout geometry
Real-World Applications
Construction: When measuring distances along a straight path, if you know distances to intermediate points, you can find total distance using segment addition.
Surveying: Along a straight survey line, if you know distances between consecutive points, you can calculate total distance.
Coordinate Systems: On a number line or coordinate axis, the segment addition postulate helps find distances between points.
Frequently Asked Questions
What is the segment addition postulate?
The segment addition postulate states that if point B is between points A and C on a line segment, then the length of AC equals the sum of lengths AB and BC: AC = AB + BC.
When can I use the segment addition postulate?
You can use it when three points A, B, and C are collinear (lie on the same line) and point B is between points A and C. If these conditions are met, AC = AB + BC.
What does "between" mean in geometry?
Point B is between A and C if all three points are collinear and B lies on the segment AC (not just on the line through A and C extended).
Can I use this with coordinates?
Yes! If points have coordinates and are collinear with B between A and C, you can find segment lengths by calculating distances between coordinates, then apply the postulate.
What if the points aren't in order?
The segment addition postulate only works when points are collinear and in the correct order (A, B, C with B between A and C). If order is different, you need to rearrange or calculate differently.
Is this the same as the angle addition postulate?
No, these are different. Segment addition postulate deals with lengths along a line. Angle addition postulate deals with angles sharing a common side. Both are fundamental geometric postulates.
Can I use this for curved lines?
No, the segment addition postulate only applies to straight line segments. For curved paths, you'd need calculus or other methods to find arc lengths.