All subjects basic Ideas Parallel lines triangle polygons Perimeter and also Area Similarity best Angles circles Geometric Solids coordinate Geometry

Closed forms or figures in a airplane with 3 or much more sides are dubbed polygons.

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Alternatively, a polygon can be defined as a close up door planar number that is the union that a finite variety of line segments. In this definition, you take into consideration closed together an unknown term. The hatchet polygon is obtained from a Greek word definition “many‐angled.”


Polygons very first fit into two basic categories— convex and not convex (sometimes called concave). Figure 1shows some convex polygons, some non‐convex polygons, and some numbers that are not also classified as polygons.

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Figure 1 Which space polygons? i m sorry of the polygons space convex?

Identifying the components of a polygon

The endpoints that the sides of polygons are referred to as vertices. once naming a polygon, that vertices are called in continually order either clockwise or counterclockwise.

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


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Figure 2 There are 4 pairs that consecutive political parties in this polygon.

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

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Figure 3Diagonals that a polygon.

Number that sides

Polygons are also classified by how many sides (or angles) they have. The adhering to lists the different species of polygons and also the number of sides the 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 an eight‐sided polygon. A nonagon is a nine‐sided polygon. A decagon is a ten‐sided polygon.

An earlier chapter proved that an it is intended triangle is immediately equiangular and also that one equiangular triangle is automatically equilateral. This walk not hold true because that polygons in general, however. Figure shows instances of quadrilaterals that are equiangular however not equilateral, equilateral however not equiangular, and equiangular and equilateral.


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

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Regular polygons

When a polygon is both equilateral and also equiangular, that is described as a regular polygon. because that a polygon to it is in regular, that must also be convex. Number shows instances of continuous polygons.