Segment Addition Postulate Calculator

Calculate segment lengths using the segment addition postulate and check if points are collinear

Calculate Segment Lengths

cm
cm

Calculation Result

Enter the required segment lengths to see the 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

1

Basic Postulate

If B lies on AC, then AB + BC = AC

2

Collinearity

Points are on the same line if the postulate holds

3

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.