The shape that is not a polygon is a circle.
Understanding Polygons
To understand why a circle isn't a polygon, let's first define what a polygon is.
Based on the provided reference, a polygon is defined as:
- A closed curve.
- Made up of only line segments.
These line segments are called sides, and they meet at points called vertices.
Why a Circle is Not a Polygon
As stated in the reference, A circle is not a polygon.
Here's why a circle doesn't fit the definition of a polygon:
- It's a closed curve: This part is true for a circle.
- Made up of only line segments: This is where a circle fails the test. A circle is a continuous curve; it does not consist of straight line segments.
Therefore, because a circle is not composed solely of straight line segments (sides), it does not meet the criteria to be classified as a polygon.
Comparing Shapes: Polygon vs. Non-Polygon
Let's look at some common shapes to highlight the difference:
| Shape | Is it a Polygon? | Why? |
|---|---|---|
| Triangle | Yes | Closed, made of 3 line segments. |
| Square | Yes | Closed, made of 4 line segments. |
| Pentagon | Yes | Closed, made of 5 line segments. |
| Circle | No | Closed, but NOT made of line segments. |
| Oval (Ellipse) | No | Closed, but NOT made of line segments. |
| Shape with curve | No | Contains a curve, not just segments. |
Shapes like triangles, squares, rectangles, pentagons, hexagons, etc., are all examples of polygons because they are closed shapes made up entirely of straight sides.
Key Takeaway
The fundamental characteristic of a polygon is that its boundary consists solely of straight line segments connected end-to-end to form a closed shape. A circle's boundary is a smooth, continuous curve, not a collection of straight lines.
