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

In an equilateral triangle all sides have the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.[1]

In an isosceles triangle, two sides are equal in length.[note 1][2] An isosceles triangle also has two angles of the same measure namely, the angles opposite to the two sides of the same length this fact is the content of the isosceles triangle theorem, which was known by Euclid. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides.[2] The latter definition would make all equilateral triangles isosceles triangles. The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles.

In a scalene triangle, all sides are unequal,[3] and equivalently all angles are unequal. Right triangles are scalene if and only if not isosceles.-Triangles can be classified according to the relative lengths of their sides:

In an equilateral triangle all sides have the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.[1]

In an isosceles triangle, two sides are equal in length.[note 1][2] An isosceles triangle also has two angles of the same measure　namely, the angles opposite to the two sides of the same length　this fact is the content of the isosceles triangle theorem, which was known by Euclid. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides.[2] The latter definition would make all equilateral triangles isosceles triangles. The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles.

In a scalene triangle, all sides are unequal,[3] and equivalently all angles are unequal. Right triangles are scalene if and only if not isosceles.