# Triangle.

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°.

In an **isosceles** triangle, two sides are equal in length. 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. 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. 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, equivalently all angles are unequal. Right triangles are scalene if and only if not isosceles.

In diagrams representing triangles (and other geometric figures), “tick” marks along the sides are used to denote sides of equal lengths – the equilateral triangle has tick marks on all 3 sides, the isosceles on 2 sides. The scalene has single, double, and triple tick marks, indicating that no sides are equal. Similarly, arcs on the inside of the vertices are used to indicate equal angles.

- One Triangle
- Two Triangles
- Three Triangles

The equilateral triangle indicates all 3 angles are equal; the isosceles shows 2 identical angles. The scalene indicates by 1, 2, and 3 arcs that no angles are equal.