# triangle

A triangle is a three-sided polygon. The sum of the interior
angles of a triangle is always 180°, unless the triangle is drawn in a non-Euclidean
geometry . Triangles can be classified either by their angles,
as **acute**, **obtuse**, or **right**;
or by their sides, as **scalene** (all different), **isosceles** (two the same), or **equilateral** (all equal). A right (or
right-angled) triangle has one interior angle equal to 90°, and may
be either scalene or isosceles (see Pythagoras'
theorem).

Various formulae link the dimensions of a triangle (see diagram). The **cosine formula** states that *a*^{ 2} = *b*^{ 2} + *c *^{2} - 2*bc* cos* A*, and the **sine formula** that *a */ sin *A* = *b */ sin *B* = *c */ sin *C*. If *s* = 1/2 (*a* + *b* + *c*), the area of the triangle is √[*s*(*s* - *a*)(*s* - *b*)(*s* - *c*)].

## Other types of triangle

A **Pythagorean triangle** is a right triangle whose sides are integers. A **primitive Pythagorean
triangle** is one whose sides are relatively
prime.

A **medial triangle** is a triangle whose vertices are the midpoints of the sides of a given triangle. An **orthic triangle** is a triangle whose vertices are the feet
of the altitudes of a given triangle.

A **limping triangle** is right triangle whose two shorter sides
(i.e., those other than the hypotenuse) differ in length by one unit. An
example is the 20-21-29 triangle (20^{2} + 21^{2} = 29^{2}).

The **pedal triangle** of a point *P* with respect to a triangle *ABC* is the triangle whose vertices are the feet
of the perpendiculars dropped from *P* to the sides of triangle *ABC*.