Definition: The common endpoint of two or more rays or line segments

Vertex typically means a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices. (Pronounced: "ver - tiss- ease"). A square for example has four vertices.

The word vertex is most commonly used to denote the corners of a polygon. For examples see:

When two lines meet at a vertex, they form an included angle. For polygons, the included angle at each vertex is an interior angle of the polygon.

Vertex is also sometimes used to indicate the 'top' or high point of something, such as the vertex of an isosceles triangle , which is the 'top' corner opposite its base, but this is not its strict mathematical definition.

The lines don't cross. The two lines that define the vertex meet at their end points. If they cross, the point where they cross is called the intersection of the two lines. It is not a vertex.

Solid Geometry

In solid geometry, a vertex is the point where three or more edges meet. In the cube below, one vertex of its possible eight is pointed out. In everyday terms, a vertex of a solid shape is a 'corner'.

Vertex of a cube, showing where three edges meet at a corner
FIG 2. Vertex of a cube. For more on cubes see Definition of a cube

Vertex of a Parabola

vertex of a parabola

A parabola is the shape defined by a quadratic equation. The vertex is the peak in the curve as shown on the right. The peak will be pointing either downwards or upwards depending on the sign of the x2 term.

For more on quadratic equations and the parabolas they define see Quadratic Explorer where you can experiment with the equation and see the effects on the resulting parabola.

Other point topics