Triangle inequality

Important

In any triangle with side lengths $a$ , $b$ , and $c$ , the triangle inequality states that the length of any side must be less than the sum of the lengths of the other two sides. This can be written as:

a < b + c

b < a + c

c < a + b

If this condition is not satisfied, the three segments cannot form a triangle.

Important properties

The triangle inequality must be true for all three sides.
If the sum of two sides equals the third, the points are collinear (they form a straight line, not a triangle).
The triangle inequality is also useful in coordinate geometry and vector problems.