Triangle Inequality Theorem Calculator with Steps

Triangle Inequality Conditions:

\[ a + b > c \] \[ b + c > a \] \[ a + c > b \]

Where a, b, c are side lengths (meters, m)

Triangle Validity:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Triangle Inequality Theorem?

Definition: The theorem states that for any three lengths to form a valid triangle, the sum of any two sides must be greater than the third side.

Purpose: This calculator helps verify whether three given lengths can form a triangle and shows the step-by-step validation process.

2. How Does the Calculator Work?

The calculator checks all three required conditions:

\[ a + b > c \] \[ b + c > a \] \[ a + c > b \]

Where:

\( a \) — Length of side A (meters)
\( b \) — Length of side B (meters)
\( c \) — Length of side C (meters)

Explanation: All three conditions must be true for the lengths to form a valid triangle.

3. Importance of Triangle Inequality

Details: This fundamental geometric principle ensures that three lengths can physically connect to form a closed shape. It's essential in construction, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter three positive lengths in meters. The calculator will verify all conditions and display detailed steps.

5. Frequently Asked Questions (FAQ)

Q1: What if two conditions pass but one fails?
A: The triangle is invalid. All three conditions must be satisfied simultaneously.

Q2: Does the order of sides matter?
A: No, the calculator checks all combinations regardless of input order.

Q3: What about degenerate triangles?
A: If any sum equals (rather than exceeds) the third side, it forms a degenerate triangle (a straight line).

Q4: Can I use different units?
A: Yes, as long as all three sides use the same unit. The calculator displays meters by default.

Q5: How precise are the calculations?
A: The calculator handles values up to two decimal places for practical applications.