Segment Addition Postulate Calculator
Calculate segment lengths using the segment addition postulate and check if points are collinear
Calculate Segment Lengths
Calculation Result
Example Calculations
Example 1: Finding Total Length
Given: AB = 5 cm, BC = 8 cm
Find: AC
Solution: AC = AB + BC = 5 + 8 = 13 cm
Example 2: Finding Partial Length
Given: AC = 15 cm, AB = 6 cm
Find: BC
Solution: BC = AC - AB = 15 - 6 = 9 cm
Example 3: Checking Collinearity
Given: AB = 4 cm, BC = 7 cm, AC = 11 cm
Check: AB + BC = 4 + 7 = 11 = AC
Result: Points are collinear ✓
Key Properties
Basic Postulate
If B lies on AC, then AB + BC = AC
Collinearity
Points are on the same line if the postulate holds
Segment Bisector
If B bisects AC, then AB = BC = AC/2
Quick Reference
Segments must be positive lengths
Point B must lie between points A and C
Useful for finding unknown segment lengths
Foundation for geometric proofs
Understanding the Segment Addition Postulate
What is the Segment Addition Postulate?
The Segment Addition Postulate is a fundamental principle in geometry that states: if point B lies on line segment AC, then the sum of the lengths of segments AB and BC equals the length of segment AC.
Mathematical Formula
AB + BC = AC
This simple yet powerful equation allows us to find unknown segment lengths when we know the other two values.
Applications
- •Finding missing segment lengths in geometric figures
- •Proving geometric theorems and properties
- •Solving real-world measurement problems
- •Checking if three points are collinear
Special Cases
Segment Bisector: If B is the midpoint of AC, then AB = BC = AC/2
Real-World Examples
🧵 Thread Cutting
Cut a thread into pieces and find the original length by adding the pieces together.
🏗️ Construction
Calculate total wall length by adding individual wall sections.
🍕 Food Sharing
Divide a sandwich length equally among friends using the segment bisector concept.