1. What is the Triangle Inequality Theorem?

The Triangle Inequality Theorem states that for any three lengths to form a triangle, the sum of any two sides must be greater than the remaining side. This fundamental geometric principle applies to all types of triangles.

2. How Does the Calculator Work?

The calculator verifies three conditions:

Where:

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

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

3. Importance of Triangle Inequality

Details: This theorem is essential in geometry, architecture, engineering, and computer graphics to verify if three given lengths can form a triangle before attempting construction or calculations.

4. Using the Calculator

Tips: Enter three positive lengths in the same units (cm shown by default). The calculator will immediately verify if they satisfy the triangle inequality conditions.

5. Frequently Asked Questions (FAQ)

Q1: Can the sides be equal?
A: Yes, equal sides form special triangles (equilateral when all equal, isosceles when two equal).

Q2: What if one condition fails?
A: Even if one inequality fails, the lengths cannot form a triangle.

Q3: Does this work for 3D triangles?
A: Yes, the theorem applies to all triangles regardless of dimension.

Q4: What about degenerate triangles?
A: When the sum equals the third side (a+b=c), it forms a degenerate (flat) triangle.

Q5: Can sides be negative or zero?
A: No, triangle sides must be positive lengths.