A **triangle** is any polygon with three sides.

## Contents

## Properties[edit | edit source]

The sum of the angles in any triangle must always be equal to 180°. Radians are not used to measure triangle angles, since they only apply to circles.

The area of any given triangle is described in this formula:

where *b* is the base of the triangle and *h* is the height of the triangle.

Hero of Alexandria is credited with the following formula. If a triangle has sides *a*, *b*, and *c*:

where *s* is the semiperimeter of the triangle, i.e. the sum of the sides divided by 2. This formula does not require knowledge of the triangle's height.

## Triangle Classifications Based On Angles[edit | edit source]

**Right**[edit | edit source]

A right triangle is any triangle with an angle of 90°.

**Special Right Triangles**[edit | edit source]

**45-45-90**[edit | edit source]

A 45-45-90 triangle is a triangle whose angles measure only 90° and 45°. Shortcuts to finding the lengths of missing sides can be found here.

- ,

so therefore,

- , or

**30-60-90**[edit | edit source]

A 30-60-90 triangle is a triangle whose angles measure only 30°, 60°, and 90°. Shortcuts to finding the lengths of missing sides can be found here.

- ,

so therefore,

- , or

**Acute**[edit | edit source]

An acute triangle is any triangle where all the angles measure less than 90°.

**Equiangular**[edit | edit source]

An equiangular triangle is an acute triangle in which all sides and angles are the same. The angles in equiangular triangles always measure 60°. This is true because 180° ÷ 3 = 60°.

**Obtuse**[edit | edit source]

An obtuse triangle is any triangle where one angle measures more than 90°.

## Triangle Classification Based On Sides[edit | edit source]

**Equilateral**[edit | edit source]

An equilateral (Latin *aequalis* "equal" + *latus* "side") triangle, also called an equiangular triangle, is an acute triangle in which all sides and angles are the same. The angles in equilateral triangles always measure 60°. This is true because 180° ÷ 3 = 60°.

**Isosceles**[edit | edit source]

An isosceles (Greek ίσος *ísos* "same" + σκελες *skeles* "legs") triangle is any triangle where 2 sides are congruent, leaving the base angles congruent as well.

**Scalene**[edit | edit source]

A scalene triangle is any triangle where no sides are congruent.