Triangles can also be classified according to their internal angles, described below using degrees of arc:

A right triangle (or right-angled triangle, formerly called a rectangled triangle) has one 90° internal angle (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle.

An oblique triangle has no internal angle equal to 90°.

An obtuse triangle is an oblique triangle with one internal angle larger than 90° (an obtuse angle).

An acute triangle is an oblique triangle with internal angles all smaller than 90° (three acute angles).

Triangles can be classified according to the relative lengths of their sides:

In an equilateral triangle, all sides are of equal length. An equilateral triangle is also an equiangular polygon, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon.

In an isosceles triangle, two sides are of equal length (originally and conventionally limited to exactly two). An isosceles triangle also has two equal angles: the angles opposite the two equal sides.

In a scalene triangle, all sides have different lengths. The internal angles in a scalene triangle are all different.

equilateral triangle

isosoles triangle

scalene triangle

right - angled triangle

obtuse triangle

acute triangle