MathSimpler
← Back to Calculator
Triangle Side Relationship

Triangle Side Relationship Calculator

Check if three side lengths can form a valid triangle using the triangle inequality theorem. Get detailed explanations and step-by-step verification.

Calculator

Quick Examples:

Results

Enter three side lengths and click "Check Triangle" to see if they can form a valid triangle.

Triangle Inequality Theorem

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This fundamental principle determines whether three given lengths can form a triangle.

The Three Conditions

a + b > c

Sum of first two sides > third side

a + c > b

Sum of first and third sides > second side

b + c > a

Sum of second and third sides > first side

Why It Works

Geometric Intuition: Imagine trying to connect three sticks end-to-end to form a triangle. If one stick is too long compared to the other two, they won't be able to meet and close the triangle.

Real-World Example: If you have sides of length 2, 3, and 10, you can't form a triangle because even when the 2 and 3 are stretched as far as possible (sum = 5), they can't reach the other end of the side with length 10.

Learn More

Explore triangle fundamentals and properties in our learning section.

Triangle Basics

Related Calculators

Try other triangle calculators for different properties.