Classification of triangles

Classifying by side lengths

Triangles can be classified according to their side lengths:

Type	Property
Equilateral	All 3 sides are of equal length
Isosceles	Exactly 2 sides are of equal length
Scalene (any)	All three sides are of different lengths

Example: a triangle with sides of 5 cm, 5 cm and 5 cm is equilateral. A triangle with sides of 5 cm, 5 cm and 8 cm is isosceles.

Classifying by angle measure

Triangles can also be classified according to their angles:

Type	Property
Acute-angled	All three angles are acute (< 90 degrees)
Right-angled	One angle measures exactly 90 degrees
Obtuse-angled	One angle is obtuse (> 90 degrees)

The special case of the equilateral triangle

An equilateral triangle always has three angles of 60 degrees (since 180 / 3 = 60). It is therefore automatically an acute-angled triangle. Similarly, an isosceles triangle always has two equal angles (those opposite the two equal sides).

Common pitfall

A triangle can be classified both by its sides AND by its angles: for example, we speak of an ‘isosceles right-angled triangle’. A common mistake is to assume that an isosceles triangle must necessarily be acute-angled, whereas an isosceles triangle may well be right-angled or even obtuse-angled, depending on the measure of its angles.