Geometric Shaped Grass Easy Polygonal Art With 10 Diferent Polygons
Table of Contents
- What is a Polygon?
- Types of Polygons
- Regular and Irregular
- Convex and Concave
- Elementary and Complex
- Names of Polygons
- Is It A Polygon?
What is a Polygon?
Polygons are some of the start shapes we acquire to draw as children, and they appear all around us. Polygons tin can be regular or irregular. They can be simple or complex, convex or concave. They can be the familiar shapes you see in geometry textbooks, or they can be strange shapes, like darts and bowties.
The word "polygon" means "many-angled," from Greek. To be a polygon, a apartment, closed shape must use only line segments to create its sides. So a circle or any shape that has a bend is not a polygon.
The 3 identifying properties of any polygon are that the polygon is:
- A ii-dimensional shape
- Endmost in a space (having an interior and outside)
- Made with straight sides
Types of Polygons
Let'south take a look at the vast assortment of shapes that are polygons and go into detail.
- A convex polygon has no interior bending greater than 180° (information technology has no inward-pointing sides). A concave polygon has 1 interior angle greater than 180°.
- A simple polygon encloses a single interior space (purlieus) and does not have self-intersecting sides. Circuitous polygons have self-intersecting sides!
- An irregular polygon does non accept congruent sides and interior angles.
- A regular polygon has congruent sides and interior angles.
Regular and Irregular Polygons
Regular polygons have coinciding sides and interior angles. Every side is equal in length to every other side, and every interior bending is equal to all other interior angles. The number of regular polygons is limitless.
Irregular polygons do non have congruent sides and angles. Home plate on a softball or baseball field is an irregular pentagon, because information technology has five sides with two 90° angles.
Convex and Concave Polygons
A convex polygon closes in an interior area without looking "dented." None of its interior angles point inward. In geometry, you lot could take a four-sided polygon that points outward in all directions, like a kite, or you could take the same four sides then 2 of them point in, forming a dart. The kite is convex; the dart is concave.
Every interior angle of a convex polygon is less than 180°. A concave polygon has at least one angle greater than 180°. Think of a bowtie-shaped simple hexagon (6 sides). It will have two interior angles greater than 180°.
Elementary and Complex Polygons
Simple polygons have no self-intersecting sides. Complex polygons, also called self-intersecting polygons, have sides that cantankerous over each other. The classic star is a complex polygon. Most people can doodle a star on paper quickly, simply few people label it a pentagram, complex polygon, or self-intersecting polygon.
The family of complex star-shaped polygons mostly share the Greek number prefix and use the suffix -gram: pentagram, hexagram, octagram, and then on.
You cannot draw a complex triangle. For every polygon with four or more sides, a complex polygon can be fatigued. A complex quadrilateral is that familiar bowtie shape, just it is considered to have only four sides, because i pair of opposite sides has twisted to cross each other.
But as you do non count the crossed sides every bit four line segments, you lot exercise non count the ii angles they create equally interior angles. The complex quadrilateral still merely has four sides and 4 interior angles.
Circuitous polygons may exist difficult to imagine unless you recollect of them with elastic sides. If y'all could elevator part of the polygon up and twist it, so ii sides cross one another, and so put it down flat over again, yous would have a complex polygon. Because you twisted two sides, you still have those two sides (they practise not double in number past crossing). They also practice not create new vertices where they cantankerous.
Antiparallelogram
An unusual circuitous polygon is the antiparallelogram, which looks a flake like bird wings. An antiparallelogram (or crossed parallelogram) has the normal 2 pairs of congruent, contrary sides, but one pair has been crossed, forming what appears to be two touching triangles.
Similar any parallelogram, though, the antiparallelogram however only has 4 sides and iv interior angles. Its diagonals, nonetheless, lie outside the shape!
Names of Polygons
| Polygon Shape | Number of Sides |
|---|---|
| Triangle | iii sides |
| Square | 4 sides |
| Rectangle | 4 sides |
| Quadrilateral | 4 sides |
| Parallelogram | 4 sides |
| Rhombus | iv sides |
| Dart | 4 sides |
| Kite | iv sides |
| Pentagon | 5 sides |
| Hexagon | half-dozen sides |
| Heptagon | seven sides |
| Octagon | 8 sides |
| Nonagon | 9 sides |
| Decagon | ten sides |
| Dodecagon | 12 sides |
| Icosagon | xx sides |
| Hectagon | 100 sides |
| northward-gon | n sides |
Is It A Polygon?
The interiors of all polygons can be broken up into triangles, which is a handy way to find the sum of their interior angles. Take two less than the number of sides, n, and multiply times 180°: (n - 2) x 180°.
A circumvolve is not a polygon, just a icosikaihenagon is a polygon. An icosikaihenagon is a 21-sided polygon. About mathematicians and mathematics students would simply write "21-gon" to name it.
Lesson Summary
Polygons can exist studied and classified in many different means. You lot now see that polygons can exist regular or irregular, convex or concave, and simple or complex. When you lot see an unfamiliar polygon, you can determine its properties and classify it correctly.
To exist a polygon, the shape must be flat, close in a infinite, and exist made using just straight sides. Polygons with congruent sides and angles are regular; all others are irregular. Polygons with all interior angles less than 180° are convex; if a polygon has at least i interior angle greater than 180°, it is concave. Simple polygons do not cross their sides; complex polygons have cocky-intersecting sides. Polygons are all around y'all!
Next Lesson:
What is a Regular Polygon?
Source: https://tutors.com/math-tutors/geometry-help/types-of-polygons
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