A **Triangle** is the 2-simplex. The study of triangles is called trigonometry. Its Bowers acronym is "trig".

## Types of Triangle

### By Sides

#### Equilateral

When all of the angles and edges of a triangle are equal a triangle is equilateral. Each angle must have a measure of exactly 60 degrees.

#### Isosceles

When a triangle has two equal sides, it is isosceles. It must also have two equal angles.

#### Scalene

A triangle with three unique side lengths is known as a scalene triangle.

### By Angles

#### Acute

A triangle with all three angles smaller than 90 degrees is called an acute triangle. All equilateral triangles are also acute triangles.

#### Right-Angled

A triangle with one right angle is a right-angled triangle. Their side lengths follow the equation

$ a^2 + b^2 = c^2 $ , where c is the edge length of the side opposite the right angle.

#### Obtuse

A triangle where at least one angle is greater than 90 degrees is called an obtuse triangle.

### Special Cases

A triangle with more than one right angle is usually degenerate, but can appear on the surface of a sphere. The same applies to a triangle with angles that sum to greater than 180 degrees, and to triangles that have any angle equal to 180 degrees.

## See Also

Zeroth | First | Second | Third | Fourth | Fifth | Sixth | Seventh | Eighth | Ninth | Tenth | Eleventh | Twelfth | Thirteenth | Fourteenth | Fifteenth | Sixteenth | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Simplex | Point | Line | Triangle
| Tetrahedron | Pentachoron | Hexateron | Heptapeton | Octaexon | Enneazetton | Decayotton | Hendecaxennon | Dodecadakon | Tredecahendakon | Quattuordecadokon | Quindecatradakon | Sexdecateradakon | Septendecapetadakon |

Hypercube | Point | Line | Square | Cube | Tesseract | Penteract | Hexeract | Hepteract | Octeract | Enneract | Dekeract | Undekeract | Dodekeract | Tredekeract | Quattuordekeract | Quindekeract | Sexdekeract |

Cross | Point | Line | Square | Octahedron | Hexadecachoron | Pentarss | Hexarss | Heptarss | Octarss | Ennearss | Decarss | Hendecarss | Dodecarss | Tredecarss | Quattuordecarss | Quindecatrarss | Sexdecaterarss |

Hypersphere | Point | Line | Circle | Sphere | Glome | Hyperglome | Hexaphere | Heptaphere | Octaphere | Enneaphere | Decaphere | Hendecaphere | Dodecaphere | Tredecaphere | Quattuordecaphere | Quindecatraphere | Sexdecateraphere |