1. What is the Triangle Inequality Theorem?

The Triangle Inequality 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. This fundamental geometric principle applies to all types of triangles.

2. How Does the Calculator Work?

The calculator checks all three conditions of the Triangle Inequality Theorem:

Where:

• \( a \) — Length of first side
• \( b \) — Length of second side
• \( c \) — Length of third side

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

3. Importance of Triangle Inequality

Details: The theorem is essential in geometry, computer graphics, navigation, and various engineering applications where triangular relationships are involved.

4. Using the Calculator

Tips: Enter positive values for all three sides in any length units (must be consistent). The calculator will verify if they satisfy the triangle inequality conditions.

5. Frequently Asked Questions (FAQ)

Q1: Can the sides be equal?
A: Yes, equal sides can form a valid triangle (equilateral or isosceles triangles).

Q2: What about degenerate triangles?
A: If a + b = c (exactly equal), it forms a degenerate triangle (collinear points), which this calculator considers invalid.

Q3: Does the order of sides matter?
A: No, the calculator checks all combinations regardless of input order.

Q4: Can I use negative values?
A: No, side lengths must be positive numbers.

Q5: What units should I use?
A: Any consistent length units (cm, inches, etc.) as long as all three sides use the same units.