How to Use Triangle Inequality Theorem Calculator
The Triangle Inequality Theorem Calculator checks whether three given side lengths can form a valid triangle. Enter the three side lengths and the calculator instantly verifies all three inequality conditions, marks each one as passed or failed, and gives a clear final verdict. The Triangle Inequality Theorem Calculator runs entirely in your browser.
- Enter side a — Type the first side length. Must be a positive number.
- Enter side b — Type the second side length. Must be a positive number.
- Enter side c — Type the third side length. Must be a positive number.
- Review the verdict — The Triangle Inequality Theorem Calculator shows each inequality check and whether the sides form a valid triangle.
Each inequality is shown with its numerical substitution so you can see the exact values being compared, not just a pass/fail label.
Formula & Theory - Triangle Inequality Theorem Calculator
The Triangle Inequality Theorem Calculator applies the Triangle Inequality Theorem, one of the most fundamental results in Euclidean geometry:
For sides a, b, c of a triangle, ALL of the following must hold:
a + b > c
a + c > b
b + c > a| Variable | Meaning |
|---|---|
| a | Length of the first side |
| b | Length of the second side |
| c | Length of the third side |
Why does this theorem work?
In a triangle, the shortest path between two vertices is the straight side connecting them. If any one side were as long as or longer than the sum of the other two, you could not “close” the triangle — the two shorter sides would not meet at a point.
Edge Cases
- All sides equal (equilateral): all three checks pass trivially.
- Two sides equal (isosceles): all checks pass as long as the unequal side is less than the sum of the two equal sides.
- Degenerate triangle (one side equals the sum of the other two): the Triangle Inequality Theorem Calculator treats this as invalid because the resulting shape would be a straight line, not a closed triangle.
Use Cases for Triangle Inequality Theorem Calculator
The Triangle Inequality Theorem Calculator is a fast, clear tool for geometry students, teachers, and anyone working with triangular shapes. Common uses include:
- Geometry homework — Verify whether a given set of side lengths forms a valid triangle before attempting further calculations.
- Test preparation — Practice identifying which condition fails when sides do not form a triangle.
- Teaching — Illustrate the Triangle Inequality Theorem with concrete numerical examples.
- Engineering and construction — Quickly check whether three measured lengths can form a triangular structural joint or framework.
The Triangle Inequality Theorem Calculator shows the full verification process step by step, helping students understand why certain side combinations work and others do not.