Triangles can be classified based on side lengths or internal angles. There are three types based on side lengths: equilateral (all sides equal), isosceles (two sides equal), and scalene (all sides different). There are also three types based on angles: right (one 90° angle), obtuse (one angle over 90°), and acute (all angles under 90°). Equilateral triangles meet criteria for both equilateral sides and acute angles.

1. Triangles can be classified according to the relative lengths of their sides:
1. 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[1]
2. In an isosceles triangle, two sides are of equal length. An isosceles triangle also has two
congruent angles (namely, the angles opposite the congruent sides). An equilateral triangle is an
isosceles triangle, but not all isosceles triangles are equilateral triangles.[2]
3. In a scalene triangle, all sides have different lengths. The internal angles in a scalene triangle
are all different.[3]
Triangles can also be classified according to their internal angles, described below using degrees
of arc:
4. 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. The other two sides are the legs or catheti (singular: cathetus) of
the triangle.
5. An obtuse triangle has one internal angle larger than 90° (an obtuse angle).
6. An acute triangle has internal angles that are all smaller than 90° (three acute angles). An
equilateral triangle is an acute triangle, but not all acute triangles are equilateral triangles.
7. An oblique triangle has only angles that are smaller or larger than 90°.