Elements of a polygon and classification

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We are going to use the previous image to define in a simple way what a polygon is.

What is a polygon?

A polygon is a geometric plane figure bounded at least by three not aligned consecutive straight segments called sides.

For instance, a pentagon is a polygon of $$5$$ sides. This is an example of a polygon of the type that we call regular.

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  • A polygon is called regular if all its sides have the same length and all its interior angles have the same measurement.
  • A polygon is irregular if it does not satisfy at least one of the previous two conditions.

These are the elements of a polygon:

  • Side: one of the segments introduced above that bounds the surface of the polygon.
  • Apex: point where two sides of the polygon intersect.
  • Diagonal: segment that connects two non adjacent apexes.
  • Angle: aperture of two adjacent segments that meet in an apex.

To be able to easily identify the elements of a polygon there exists a very simple notation that helps us to know which element we are speaking about at any moment. This way we will be able to differentiate the sides, apexes or any other element.

Let's see an example and then we will explain the exact notation.

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Notation

In the previous example we have an irregular polygon of $$5$$ sides ($$5$$ apexes). We can see that every apex is named by a letter $$A, B, C, D, E$$. We can do this with all the letters that we should need. It is not necessary for these letters to follow the order of the alphabet. Nevertheless, it is advisable in order to make the notation easier.

The segments that connect two apexes, the sides, are called by the letters corresponding to the apexes that they connect. For instance, the side that connects the apexes $$C$$ and $$B$$ would be called: side $$BC$$. We should try, when naming the sides, to put the letters in alphabetical order, but this is not absolutely necessary. If we want to refer to the segment, we will use square brackets, for example $$[BC]$$ and if we are talking about the straight line that passes by the apexes we will use brackets, for example, $$(BC)$$.

The angles are denoted by using the letter corresponding to the apex with which they are associated, but while adding a circumflex over the letter. For example, the angle associated with the apex $$E$$ is denoted for $$\widehat{E}$$.

The diagonals are denoted just as the sides. For example, the diagonal that connects the apexes $$A$$ and $$C$$ is denoted by $$[AC]$$.

Classification

Let's see now the classification of the regular polygons as its number of sides:

Name Number of sides
It does not exist 1
It does not exist 2
Triangle 3
Square 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Enneagon 9
Decagon 10