Definition:Triangle (Geometry)

Definition
A triangle (or, rarely, trigon) is a polygon with three sides.

Because it is a polygon, it follows that it also has three vertices and three angles.

Adjacent
The two sides of the triangle which form a particular angle are referred to as adjacent to that angle.

Similarly, the two angles of a triangle to which a particular side contributes are referred to as adjacent to that side.

Opposite
The side of the triangle which is not one of the sides adjacent to a particular angle is referred to as its opposite.

Thus, each angle has an opposite side, and each side has an opposite angle.

Base
For a given triangle, one of the sides can be distinguished as being the base. It is immaterial which is so chosen. The usual practice is that the triangle is drawn so that the base is made horizontal, and at the bottom.

Apex
Having chose one side as the base, the opposite angle is called the apex.

Height
The height of a triangle is the length of a perpendicular from the apex to the base.

Otherwise known as the altitude.

Conventional Nomenclature

 * Triangle.png

The vertices of the triangle are conventionally labeled $A, B, C$ (or with other uppercase letters), and the sides with lowercase letters corresponding to the opposite angle, as above.

In order to emphasize that a particular angle being referred to is in fact an angle, the symbol $\angle$ is often placed by the letter corresponding to that angle.

Thus, for example:
 * $\angle A$ is adjacent to sides $b$ and $c$;
 * Side $a$ is adjacent to $\angle B$ and $\angle C$;
 * $\angle A$ is opposite side $a$;
 * Side $a$ is opposite $\angle A$.

Scalene Triangle
A scalene triangle is a triangle in which all three sides are different lengths.


 * ScaleneTriangle.png

Oblique Triangle
An oblique triangle is a triangle in which none of the angles are right angles.

Acute-Angled Triangle
An acute-angled triangle, or an acute triangle, is a triangle in which all three of the angles are acute angles.

Obtuse-Angled Triangle
An obtuse-angled triangle, or an obtuse triangle, is a triangle in which one of the angles is a obtuse angle.

Also see

 * Area of Triangle

Euclid's Definition