Triangle Inequality Theorem Calculator

What is the Triangle Inequality Theorem?

The Triangle Inequality Theorem is like a rule for building triangles. It says that the sum of any two sides of a triangle must be greater than the third side. It's like saying you can't make a triangle with a really long stick and two tiny ones!

How to Use the Triangle Inequality Theorem

To use this theorem, we check if the sum of any two sides is greater than the third side. We do this for all three combinations of sides. If all three checks pass, we can make a triangle!

Formula

For a triangle with sides \(a\), \(b\), and \(c\), we check:

\[ a + b > c \]

\[ b + c > a \]

\[ c + a > b \]

Where:

• \(a\), \(b\), and \(c\) are the lengths of the three sides of the triangle

Calculation Steps

1. Add the lengths of sides a and b
2. Check if this sum is greater than side c
3. Repeat steps 1 and 2 for sides b and c, and then for c and a
4. If all three checks pass, you can form a triangle!

Example and Visual Representation

Let's try with sides: a = 3, b = 4, c = 5

Check 1: 3 + 4 = 7 > 5 ✓

Check 2: 4 + 5 = 9 > 3 ✓

Check 3: 5 + 3 = 8 > 4 ✓

All checks pass, so we can make a triangle!

This picture shows our triangle. The sides 3, 4, and 5 fit together perfectly to make a right-angled triangle!