Polygon Vertex — Definition, Formula & Examples
A polygon vertex is a corner point where two sides of a polygon meet. Every polygon has the same number of vertices as it has sides.
A vertex of a polygon is a point at which two consecutive edges of the polygon intersect. For an -sided polygon (an -gon), there are exactly vertices.
How It Works
To find the vertices of a polygon, look for the corner points where two sides come together. A triangle has 3 vertices, a quadrilateral has 4, a pentagon has 5, and so on. Vertices are usually labeled with capital letters like , , . These labels help you name the polygon (for example, "quadrilateral ") and describe its diagonals, angles, and other features. The angle formed at a vertex by the two sides meeting there is called an interior angle of the polygon.
Worked Example
Problem: A regular hexagon has vertices labeled A, B, C, D, E, and F. How many vertices does it have, and how many diagonals can be drawn from vertex A?
Count the vertices: A hexagon has 6 sides, so it has 6 vertices.
Find diagonals from vertex A: From vertex A, you cannot draw a diagonal to A itself or to the two adjacent vertices (B and F), since those segments are sides, not diagonals. That leaves 3 other vertices.
Answer: The hexagon has 6 vertices, and 3 diagonals can be drawn from vertex A (to vertices C, D, and E).
Why It Matters
Vertices are the foundation for describing polygon properties like interior angles, diagonals, and symmetry. In coordinate geometry, you define a polygon entirely by listing the coordinates of its vertices, which lets you calculate perimeter, area, and other measurements.
Common Mistakes
Mistake: Confusing "vertex" with "side" when counting polygon features.
Correction: A vertex is a point (corner), while a side is a line segment connecting two consecutive vertices. An -gon always has vertices and sides.