In geometry, a vertex is defined as a point where two or more lines, edges, or rays converge.

More specifically, a vertex is a fundamental concept in geometry that aids in understanding the shapes and structures of various figures. For instance, in a triangle, each of the three corners is referred to as a vertex. Likewise, in a square, there are four vertices, one located at each corner where the sides intersect. The plural form of vertex is vertices.

The concept of vertices extends beyond two-dimensional shapes. In three-dimensional geometry, a vertex is the point where the edges of a polyhedron meet. For example, a cube has eight vertices, with one at each corner where three edges converge. Grasping the concept of vertices is essential for analyzing and describing the properties of geometric shapes, including angles, edges, and faces.

In coordinate geometry, a vertex can be represented by a set of coordinates. In two dimensions, this can be expressed as $(x, y)$, while in three dimensions, it is represented as $(x, y, z)$. These coordinates enable us to precisely locate the vertex within a plane or space. For example, the vertex of a parabola in its standard form, $y = ax^2 + bx + c$, can be determined using the formula

Vertices are also crucial in graph theory, where they represent nodes or points within a network. A solid understanding of the concept of a vertex is vital for solving problems related to shapes, structures, and networks, making it a key component of GCSE Mathematics.