Table that Contents

What is a Polygon?

Polygons are some of the very first shapes we discover to attract as children, and also they show up all around us. Polygons deserve to be regular or irregular. They deserve to be an easy or complex, convex or concave. They can be the acquainted shapes you check out in geometry textbooks, or they deserve to be weird shapes, favor darts and also bowties.

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The indigenous "polygon" means "many-angled," native Greek. To be a polygon, a flat, closed shape have to use just line segments to develop its sides. So a circle or any shape that has actually a curve is not a polygon.

The three identifying properties of any kind of polygon space that the polygon is:

A two-dimensional form Closing in a space (having an interior and exterior) do with straight sides

Types the Polygons

Let"s take a look in ~ the substantial array of forms that room polygons and also go into detail.


A convex polygon has no interior angle greater than 180° (it has no inward-pointing sides). A concave polygon has actually one inner angle higher than 180°.A simple polygon encloses a single interior an are (boundary) and also does not have self-intersecting sides. Complicated polygons have self-intersecting sides!An irregular polygon walk not have congruent sides and also interior angles.A regular polygon has congruent sides and also interior angles.


Regular and also Irregular Polygons

Regular polygons have actually congruent sides and interior angles. Every side is same in size to every various other side, and every internal angle is equal to all other inner angles. The variety of regular polygons is limitless.

Irregular polygons do not have congruent sides and also angles. House plate ~ above a soft ball or baseball field is an rarely often, rarely pentagon, due to the fact that it has five sides with two 90° angles.


Convex and also Concave Polygons

A convex polygon close the door in an inner area there is no looking "dented." none of its inner angles allude inward. In geometry, you could have a four-sided polygon that points external in every directions, prefer a kite, or you can have the same four sides so two of them point inward, forming a dart. The kite is convex; the dart is concave.


Every internal angle of a convex polygon is much less than 180°. A concave polygon contends least one angle greater than 180°. Think that a bowtie-shaped basic hexagon (6 sides). The will have two inner angles better than 180°.


Simple and complicated Polygons

Simple polygons have no self-intersecting sides. Complex polygons, likewise called self-intersecting polygons, have sides that cross end each other. The classic star is a complicated polygon. Most world can doodle a star on paper quickly, but few people brand it a pentagram, complicated polygon, or self-intersecting polygon.


You cannot attract a facility triangle. For every polygon with 4 or much more sides, a complicated polygon can be drawn. A complex quadrilateral is that familiar bowtie shape, but it is considered to have actually only 4 sides, since one pair of the contrary sides has twisted come cross each other.

Just together you do not count the crossed political parties as 4 line segments, you perform not count the 2 angles they create as internal angles. The facility quadrilateral still only has four sides and also four interior angles.


Complex polygons might be difficult to imagine uneven you think the them with elastic sides. If you can lift part of the polygon up and twist it, so two sides overcome one another, and then put it down flat again, you would have actually a facility polygon. Since you twisted 2 sides, girlfriend still have actually those two sides (they execute not dual in number by crossing). They likewise do not create new vertices whereby they cross.


An unusual facility polygon is the antiparallelogram, which looks a bit like bird wings. One antiparallelogram (or crossed parallelogram) has actually the normal 2 pairs the congruent, the contrary sides, however one pair has been crossed, developing what appears to be two poignant triangles.


Like any type of parallelogram, though, the antiparallelogram still only has four sides and four internal angles. That is diagonals, however, lie outside the shape!

Names the Polygons

Names of PolygonsPolygon ShapeNumber that Sides
Triangle3 sides
Square4 sides
Rectangle4 sides
Quadrilateral4 sides
Parallelogram4 sides
Rhombus4 sides
Dart4 sides
Kite4 sides
Pentagon5 sides
Hexagon6 sides
Heptagon7 sides
Octagon8 sides
Nonagon9 sides
Decagon10 sides
Dodecagon12 sides
Icosagon20 sides
Hectagon100 sides
n-gonn sides

Is that A Polygon?

The interiors of every polygons can be damaged up right into triangles, i m sorry is a handy means to uncover the sum of their internal angles. Take two much less than the number of sides, n, and also multiply time 180°: (n - 2) x 180°.


A one is no a polygon, yet a icosikaihenagon is a polygon. One icosikaihenagon is a 21-sided polygon. Most mathematicians and mathematics college student would simply write "21-gon" to name it.

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Lesson Summary

Polygons have the right to be studied and also classified in countless different ways. You now see that polygons deserve to be constant or irregular, convex or concave, and basic or complex. As soon as you see an unfamiliar polygon, you can determine the properties and also classify the correctly.

To it is in a polygon, the shape must be flat, near in a space, and be make using only straight sides. Polygons v congruent sides and also angles space regular; all others room irregular. Polygons v all internal angles less than 180° are convex; if a polygon has at least one inner angle greater than 180°, it is concave. Simple polygons execute not cross your sides; facility polygons have actually self-intersecting sides. Polygons room all around you!

Next Lesson:

What is a continual Polygon?

What you learned:

After viewing the video, reading these notes, and also studying the drawings, you will discover to:

Define a polygon recognize its identifying properties Distinguish between regular and also irregular polygons, basic and complicated polygons, and concave and also convex polygons Draw and also recognize instances of every the species of polygon