# Identifying right-angled triangles

**Identifying right-angled triangles**

The Pythagoras theorem is only applicable to right angled triangles therefore we can use this formula to work out if a triangle contains a right angle. For example:

A triangle has the sides of length of: 4 cm, 7 cm and 9 cm.

*c*² = *a*² – *b*²

9² = 4² – 7²

9² ≠ 65

Therefore this is not a right angled triangle.

**Identifying right-angled triangles**

The following rules apply when identifying right-angled triangles:

- If the sum of the squares on the two shortest sides of a triangle is more than the sum of the square on the longest side, all angles must be acute. Therefore

*c*² < *a*² + *b*²

- If the sum of the squares on the two shortest sides of a triangle is less than the sum of the square on the longest side,
**one**of the angles in the triangle is obtuse. Therefore

*c*² > *a*² + *b*²