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Closed shapes or figures in a plane with 3 or an ext sides are called polygons.

You are watching: A polygon that is both equilateral and equiangular

Alternatively, a polygon have the right to be defined as a closed planar figure that is the union of a finite variety of line segments. In this definition, you consider closed together an unknown term. The term polygon is acquired from a Greek word definition “many‐angled.”

Polygons an initial fit into two general categories— convex and also not convex (sometimes dubbed concave). Number 1shows part convex polygons, some non‐convex polygons, and some numbers that space not even classified together polygons.

Figure 1 Which space polygons? which of the polygons are convex?

## Identifying the parts of a polygon

The endpoints that the sides of polygon are called vertices. as soon as naming a polygon, its vertices are called in consecutive order either clockwise or counterclockwise.

Consecutive sides room two sides that have an endpoint in common. The four‐sided polygon in Figure could have been named ABCD, BCDA, or ADCB, for example. It does not issue with i m sorry letter you start as long as the vertices are called consecutively. Sides AB and BC are examples of continuous sides.

Figure 2 There are 4 pairs of consecutive sides in this polygon.

A diagonal of a polygon is any type of segment the joins two nonconsecutive vertices. Figure 3shows five‐sided polygon QRSTU. segments QS , SU , UR , RT and QT are the diagonals in this polygon.

Figure 3Diagonals of a polygon.

## Number of sides

Polygons are also classified by how numerous sides (or angles) castle have. The following lists the different types of polygons and the number of sides that they have:

A triangle is a three‐sided polygon. A quadrilateral is a four‐sided polygon. A pentagon is a five‐sided polygon. A hexagon is a six‐sided polygon. A septagon or disappearance is a seven‐sided polygon. One octagon is one eight‐sided polygon. A nonagon is a nine‐sided polygon. A decagon is a ten‐sided polygon.

An earlier chapter proved that an equilateral triangle is immediately equiangular and that one equiangular triangle is automatically equilateral. This does not host true for polygons in general, however. Number shows instances of square that room equiangular yet not equilateral, equilateral but not equiangular, and equiangular and equilateral.

Figure 4 An equiangular quadrilateral does not have to be equilateral, and an equilateral square does not have to be equiangular.

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## Regular polygons

When a polygon is both equilateral and also equiangular, that is referred to as a regular polygon. for a polygon to it is in regular, that must likewise be convex. Figure shows instances of consistent polygons.