Triangles: definitions and classification
What is a triangle?
A shape has three sides
A triangle is a closed geometric shape consisting of 3 vertices, 3 sides (line segments) and 3 angles. It is often named using the letters of its vertices, for example, triangle ABC.
Basic vocabulary
| Element | Definition |
|---|---|
| Vertex | Point where two sides meet (A, B, C) |
| Side | Line segment connecting two vertices (e.g. [AB]) |
| Angle | The angle formed by two sides that intersect at a vertex |
The sum of the angles
In ANY triangle, regardless of its shape, the sum of the three interior angles is always 180 degrees.
Example: if a triangle has one angle of 50 degrees and another of 70 degrees, the third angle is: 180 – 50 – 70 = 60 degrees.
Perimeter
The perimeter of a triangle is the sum of its three sides: P = AB + BC + CA.
Example: if AB = 4 cm, BC = 5 cm and CA = 6 cm, then P = 4 + 5 + 6 = 15 cm.
Common pitfall
Do not confuse an angle with a vertex: a vertex is a point, whereas an angle is a measure (in degrees) associated with that point. Many pupils also forget that the sum of the angles is constant (180 degrees): it never depends on the size of the triangle, only on its type (whether it is a right-angled, isosceles, etc. triangle makes no difference to this total).