Polygons and Non-Polygons

A polygon is a flat, closed shape that is made up only of straight sides. The sides connect end to end so there are no gaps, and none of the sides curve. Triangles, squares, rectangles, and pentagons are all polygons because every one of their sides is straight and the shape closes up completely.

Two rules decide whether a shape is a polygon:

• Every side must be a straight line, not a curve.
• The shape must be closed, meaning the sides connect all the way around with no gaps or crossing lines.

If you already know how to count the sides and corners of 2D shapes, spotting a polygon becomes even easier, since a polygon always has at least three straight sides and the same number of corners.

A non-polygon is any shape that breaks one of the two polygon rules. A shape is a non-polygon if it has at least one curved side, like a circle or an oval, or if it is not fully closed, like a shape with a gap where the sides never meet, or if its lines cross over each other in a way that does not form a simple closed outline.

Here is a simple side-by-side look at some polygons and some non-polygons.

Looking at everyday shapes helps make the rules stick. Here are some quick examples.

• Polygons: triangle, square, rectangle, pentagon, hexagon, and any shape with straight sides that close up.
• Non-polygons: circle, oval, crescent moon shape, and any shape with at least one curve or an open gap.
• Tricky case: a shape that looks closed but has one rounded corner is still a non-polygon, because every side and corner in a polygon must be straight.

This lesson focuses on telling polygons apart from non-polygons. For a broader look at naming and describing flat shapes in general, see introduction to 2D shapes. Solid shapes such as cubes and cones follow different rules altogether, which you can explore in comparing 2D and 3D shapes.

When you are not sure about a shape, ask two questions in order.

1. Are all of its sides straight? If any side curves, it is a non-polygon.
2. Does the shape close up completely with no gaps and no crossing lines? If not, it is a non-polygon.

If the shape passes both checks, it is a polygon. Practicing this two-step test on a mix of pictures, some with straight sides, some with curves, and some with open ends, is the fastest way to build confidence in sorting polygons and non-polygons correctly.

Related lessons

• Math 3