Triangles are polygons with three sides, and three corners. The three corners of a triangle always add up to 180°, however the angle of each of those corners can vary, as can the length of the sides, within the confines that the angles of the triangle must add up to 180°.

Figure 1: The 6 types of triangle. Equilateral, isosceles and scalene triangles are defined in reference to the length of the sides. Acute, right and obtuse triangles are defined in reference to the angle of the corners.

All triangles have many similarities and common properties aside having three sides. All of them also have three corners, and the angles of those corners all add up to 180°. The different types of triangle can be described in terms of the length of their sides, or in terms of their corners, so triangles can be two types of triangle at the same time. These types of triangle (Figure 1) are defined as follows: Equilateral – All three sides of an equilateral triangle are the same length, and all three corners have the same angle (60°).

Isosceles – In an isosceles triangle, two of the sides are the same length, while the third is different. Additionally, two of the corners are at the same angle.

Scalene – In a scalene triangle, all sides are of different lengths, and consequently all the corners have different angles.

Acute – In an acute triangle, all corners have angles which are less than 90°, so that all the angles are acute angles.

Right [angled] – In a right triangle, one of the corners of the triangle has a 90° angle. This gives this type of triangle some special properties not found in other triangles. The properties of right triangles apply whether or not the other two corners are the same angle (and if they are both the same angle, they are also an isosceles triangle) as the key thing that gives them these properties is the right angle, the key thing which gives them their properties is the right angle. In British English, these are called right angled triangles.

Obtuse – In an obtuse triangle, one of the angles is greater than 90°. Only one angle can be greater than 90° due to the total of the angles equaling 180°.

The mathematics that describes triangles is called trigonometry. As triangles are a shape found in a lot of structures, a lot of the same trigonometry techniques can be applied to other shapes and structures which contain or a built from triangles.

Figure 2: The corners of a triangle are labelled with capital letters A, B, and C. The opposite sides of these corners are labelled with the lower case letters a, b, and c. This allows for trigonometric laws such as the sine law or the cosine law to describe how the sides and corners of a triangle relate to one another.

The sides and angles in triangles are described in a standard format (Figure 2). The corners are described using the capital letters A, B and C, whereas the sides are described using the lower case letters a, b and c. This consistent format for describing the sides and corners of triangles allows the sine, cosine and tangent laws to be described clearly.