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Home » Polygons » What are Polygons?

What are Polygons?

Last updated: Mar 27, 2021 by Ido Sarig · This website generates income via ads and uses cookies · Terms of use · Privacy policy

In today's lesson, we'll ask what are polygons in geometry. We'll also discuss types of polygons - regular, simple, complex, and more.

Definition

A polygon is a two-dimensional (flat) shape. We create polygons by connecting a number of straight lines to form a closed shape. Circles and ellipses are not polygons, because their edges are not straight lines.

We name polygons according to the number of sides they have. That is, the number of straight-line segments that are used in drawing the shape. A polygon with three sides is a triangle. A polygon with four sides is a quadrangle, and so on.

Types of polygons

Regular polygons

If all the sides of a polygon are of equal length, and all its angles have the same measure, we call it ‘regular’.

Simple polygons

Simple polygons have sides that do not intersect or cross each other:

What are Polygons? A simple polygon

Complex polygons

Complex polygons have sides that intersect, for example:

complex polygon

Convex polygons

Convex polygons are simple polygons where all the interior angles measure less than 180°. The polygons vertices point "outward" from its center.

Convex polygon

Concave polygons

In Concave polygons, there is at least one interior angle which measure more than 180°:

Concave Polygon

Our focus: simple convex polygons

We will only concern ourselves with simple convex polygons. It is rare to see high school geometry problems that involve concave polygons, and even rarer to see ones involving self-intersecting polygons.

In addition, even those problems that do involve such polygons typically have answers that involve treating those complex polygons as a number of simple polygons side by side. For example, look at the complex polygon illustrated above. In most cases, we could simply treat it as if it was a triangle connected to a quadrilateral at one point of intersection.

« Lines and Angles in Geometry
Sum of Angles in a Triangle »

About the Author

Ido Sarig is a high-tech executive with a BSc degree in Computer Engineering. His goal is to help you develop a better way to approach and solve geometry problems. You can contact him at [email protected]

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About

Welcome to Geometry Help! I'm Ido Sarig, a high-tech executive with a BSc degree in Computer Engineering and an MBA degree in Management of Technology. I'm here to tell you that geometry doesn't have to be so hard! My goal with this website is to help you develop a better way to approach and solve geometry problems, even if spatial awareness is not your strongest quality. Read More…

Geometry Topics

  • Area of Geometric Shapes
  • Circles
    • Arcs, Angles, and Sectors
    • Chords
    • Inscribed Shapes
    • Tangent Lines
  • Lines and Angles
    • Intersecting Lines and Angles
    • Parallel Lines
    • Perpendicular lines
  • Pentagons and Hexagons
  • Perimeter of Geometric Shapes
  • Polygons
  • Quadrangles
    • Kites (Deltoids)
    • Parallelograms
    • Rectangles
    • Rhombus
    • Squares
    • Trapezoids
  • Triangles
    • Congruent Triangles
    • Equilateral Triangles
    • Isosceles Triangles
    • Pythagorean Theorem
    • Right Triangles
    • Similar Triangles
    • Triangle Inequalities

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