📐 Triangle Inequality Theorem Calculator
Check if three side lengths can form a triangle
How to Use This Calculator
Enter Three Side Lengths
Input the lengths of all three sides (a, b, c).
Check
Click "Check Triangle Inequality" to verify if the sides can form a triangle.
Review Results
See if the sides can form a triangle and which inequality conditions are met or violated.
Triangle Inequality Theorem
For sides a, b, c to form a triangle:
a + b > c, a + c > b, and b + c > a
Theorem Statement:
Three side lengths can form a triangle if and only if the sum of any two sides is greater than the third side.
All Three Conditions Must Be True:
- a + b > c
- a + c > b
- b + c > a
Why This Works:
If one side is too long, the other two sides cannot "meet" to form a closed triangle. They would either be parallel or diverge.
About Triangle Inequality Theorem Calculator
The Triangle Inequality Theorem Calculator checks whether three given side lengths can form a valid triangle. According to the theorem, three sides can form a triangle only if the sum of any two sides is greater than the third side.
When to Use This Calculator
- Geometry: Verify if side lengths form a valid triangle
- Construction: Check triangle dimensions before building
- Education: Learn and practice the triangle inequality theorem
- Problem Solving: Validate triangle problems
Why Use Our Calculator?
- ✅ Quick Verification: Instantly check triangle validity
- ✅ Detailed Analysis: Shows which conditions pass or fail
- ✅ Visual Feedback: Clear indication of results
- ✅ Educational: Helps understand the theorem
- ✅ Free: No registration required
Key Concepts
- Necessary Condition: All three inequalities must be satisfied
- Degenerate Case: If a + b = c (equality), the triangle is degenerate (flat)
- Intuitive Meaning: No single side can be as long as or longer than the sum of the other two
Frequently Asked Questions
What is the triangle inequality theorem?
The triangle inequality theorem states that for three side lengths to form a triangle, the sum of any two sides must be greater than the third side: a + b > c, a + c > b, and b + c > a.
What if two sides equal the third?
If a + b = c (or similar), the triangle is degenerate (flat) - all three points lie on a straight line. This is not considered a valid triangle.
Do all three conditions need to be checked?
Yes! While one condition is often sufficient (checking the largest side), all three must hold. However, if sides are sorted, checking min + mid > max is sufficient.
Can negative numbers form a triangle?
No! Side lengths must be positive numbers. Negative or zero lengths don't make geometric sense for triangles.