Triangle Inequality Theorem

Any side of a triangle must be shorter than the other two sides added together.

Why? Well imagine one side is not shorter:

• If a side is longer than the other two sides there is a gap:



• If a side is equal to the other two sides it is not a triangle (just a straight line back and forth).

Try moving the points below:

When the three sides are a, b and c, we can write:

• a < b + c
• b < a + c
• c < a + b