1. What is the Triangle Inequality Theorem?

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. This fundamental principle determines whether three given lengths can form a triangle.

2. How Does the Calculator Work?

The calculator checks all three conditions of the theorem:

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 three lengths to form a valid triangle.

3. Importance of Triangle Inequality

Details: This theorem is essential in geometry, construction, computer graphics, and any field where triangle validity must be verified. It's the fundamental check before attempting to construct a triangle.

4. Using the Calculator

Tips: Enter positive values for all three sides in the same units. The calculator will verify if they satisfy all triangle inequality conditions.

5. Frequently Asked Questions (FAQ)

Q1: Can the sides be equal?
A: Yes, equilateral triangles have all sides equal (a = b = c), and isosceles triangles have two equal sides.

Q2: What if one condition fails?
A: If any one of the three inequalities fails, the sides cannot form a triangle.

Q3: Does this work for degenerate triangles?
A: No, this calculator checks for valid (non-degenerate) triangles where the sum cannot equal the third side.

Q4: What units should I use?
A: Any consistent length unit (cm, m, inches, etc.) as long as all three sides use the same unit.

Q5: Can this determine triangle type?
A: While it checks validity, additional calculations would be needed to determine if the triangle is acute, right, or obtuse.