What is the location of vertices?

A polygon, in its two-dimensional form, comprises various elements that define its shape and structure. One of these essential components is the vertex, which plays a pivotal role in defining the polygon's geometry.

A vertex, quite simply, represents the point where two adjacent sides of a polygon intersect. This intersection creates a distinct corner, which can be visually identified as a turning point in the polygon's outline.

When considering polygons, it is essential to acknowledge the inherent relationship between the number of sides and vertices. This relationship is fundamental to understanding the polygon's overall composition.

Specifically, in any polygon, regardless of its size, shape, or complexity, the number of sides it possesses is equal to the number of vertices it contains. This equality underscores the interconnectedness and balance inherent in polygonal geometry.

For instance, in a triangle, which is the simplest Polygon with three sides, there are also three vertices—one at each corner where the sides intersect. Similarly, a quadrilateral, with four sides, has four vertices, and this pattern continues for polygons of any size.