The number of vertices in any polygon is always equal to its number of sides.
A polygon is a closed two-dimensional shape made up of straight line segments. These segments are called sides or edges, and they connect at points known as vertices, which are the corners of the shape. The direct correspondence between the number of sides and the number of vertices is a defining characteristic of all polygons.
Understanding Polygon Vertices
A vertex (plural: vertices) is a fundamental component of any polygon. It is the point where two adjacent sides meet, forming an angle. For instance, a triangle, by its very nature, has three sides and consequently, three vertices. This consistent relationship simplifies the identification and classification of polygons.
Vertices in Common Polygons
Here is a clear breakdown of the number of vertices for several common polygons:
| Names of Polygon | No. of Vertices |
|---|---|
| Triangle | 3 |
| Quadrilateral | 4 |
| Pentagon | 5 |
| Hexagon | 6 |
As demonstrated in the table, the prefix in a polygon's name often indicates its number of sides, which directly corresponds to its number of vertices. For example, "tri-" denotes three, "quad-" refers to four, "penta-" signifies five, and "hexa-" means six.
What is a Polygon?
Polygons are foundational geometric figures defined by their specific characteristics. They are flat, closed shapes bounded by straight line segments. Understanding their properties is crucial in geometry.
Key characteristics that define a polygon include:
- Closed Figure: All sides connect end-to-end, forming an enclosed region without any gaps.
- Straight Sides: Polygons are constructed solely from straight line segments; no curves are permitted.
- Two-Dimensional: They exist on a single plane.
- Non-Intersecting Sides: The sides of a polygon only meet at their endpoints (vertices), never crossing over each other in the middle.
For further exploration of polygons and their various properties, you can consult comprehensive mathematical resources. For instance, Wikipedia provides a detailed overview of polygons.
