Angles and PolygonsIntroduction to Polygons

Look around you — you will see shapes everywhere! The screen you are reading on is a rectangle, the stop sign on the road is an octagon, and the honeycomb in a beehive is made of hexagons. All of these shapes have something in common: they are all polygons.

A polygon is a closed shape made entirely of straight line segments. The word comes from Greek: poly means "many" and gon means "angle".

Which of these shapes are polygons? Continue

A circle is not a polygon because it has curved sides. An open shape is not a polygon because it is not fully closed. A shape with curves is not a polygon because polygons are made only of straight line segments.

Every polygon has two important parts:

• The straight line segments that form the outline are called sides (or edges).
• The points where two sides meet are called vertices (singular: vertex).

Move the vertices of the polygon below and notice how the number of sides always equals the number of vertices.

A polygon with n sides always has exactly vertices.

Polygons are named based on the number of their sides. Here are the most common ones:

The names come from Greek and Latin: tri = 3, quad = 4, penta = 5, hex = 6, octa = 8. Continue

A diagonal is a line segment that connects two non-adjacent vertices of a polygon. Click on the tabs below to see the diagonals of different polygons:

A quadrilateral has diagonals. A pentagon has diagonals. A hexagon has diagonals.

For a polygon with n sides, the number of diagonals is nn−32. Each vertex connects to n−3 other vertices (not itself, and not its two neighbors), and we divide by 2 because each diagonal is counted twice.