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POLYGONS “MANY” “SIDES” A polygon is a 2-dimensional shape. This means that polygons have both length and width. L E N G T H WIDTH Polygons are closed shapes, and they are made of at least 3 line segments. Why is this shape NOT a polygon? This shape is NOT “closed.”

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POLYGONS

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Polygons l.jpg

POLYGONS

“MANY” “SIDES”


A polygon is a 2 dimensional shape l.jpg

A polygon is a 2-dimensional shape.


This means that polygons have both length and width l.jpg

This means that polygons have both length and width.

L

E

N

G

T

H

WIDTH


Polygons are closed shapes and they are made of at least 3 line segments l.jpg

Polygons are closed shapes, and they are made of at least 3 line segments.


Why is this shape not a polygon l.jpg

Why is this shape NOT a polygon?


This shape is not closed l.jpg

This shape is NOT “closed.”


Why can t a polygon have only 2 sides l.jpg

Why can’t a polygon have only 2 sides?


With only 2 sides the shape could not be closed l.jpg

With only 2 sides, the shape could not be “closed.”


Is this shape a polygon l.jpg

Is this shape a polygon?


As a matter of fact this is a polygon l.jpg

As a matter of fact, this IS a polygon.


This shape is closed and it has 12 sides l.jpg

This shape is “closed,” and it has 12 sides.


However this is a special type of polygon called concave l.jpg

However, this is a special type of polygon called “concave.”


It s called concave because some of the sides are caved in l.jpg

It’s called “concave” because some of the sides are “caved in.”


For our purposes we will be discussing only convex polygons and not concave polygons l.jpg

For our purposes, we will be discussing only convex polygons and not concave polygons.


We will learn the names for the first eight polygons l.jpg

We will learn the names for the first eight polygons.


A one sided polygon is called l.jpg

A one-sided polygon is called…?


Slide17 l.jpg

That’s a trick question. There is no such thing as a one-sided polygon. Remember, polygons must have at least 3 sides.


A 3 sided polygon is called a triangle l.jpg

A 3-sided polygon is called a triangle.


You can remember the prefix tri by thinking of a tricycle a tricycle has 3 wheels l.jpg

You can remember the prefix “tri” by thinking of a tricycle. A tricycle has 3 wheels.


A 4 sided polygon is called a quadrilateral l.jpg

A 4-sided polygon is called a quadrilateral.


You can remember the prefix quad by thinking times four l.jpg

You can remember the prefix “quad” by thinking “times four.”

Quadruple means x 4


A 5 sided polygon is called a pentagon l.jpg

A 5-sided polygon is called a pentagon.


You can remember this name by thinking about the building in washington d c l.jpg

You can remember this name by thinking about the building in Washington, D.C.


A six sided polygon is called a hexagon l.jpg

A six-sided polygon is called a hexagon.


Slide25 l.jpg

You can remember that a hexagon has six sides because the words hexagon and six both have the letter “x.”


The hexagon is the polygon of choice for bees l.jpg

The hexagon is the polygon of choice for bees.


A 7 sided polygon is called a heptagon l.jpg

A 7-sided polygon is called a heptagon.


You can remember the prefix hept by thinking of the heptathalon in the olympics l.jpg

You can remember the prefix “hept” by thinking of the heptathalon in the Olympics.

heptathlon—a two-day event in which athletes compete in the 100-meter hurdles, high jump, shot put, and 200-meter dash on the first day and in the long jump, javelin, and 800-meter race on the second day.


Slide29 l.jpg

Joyner-Kersee, JackieJoyner-Kersee, Jackie (1962- ), American track-and-field athlete, who won the heptathlon event (an all-around event) at the Olympic Games in 1988 and 1992. She is considered one of the greatest female athletes.


An 8 sided polygon is called an octagon l.jpg

An 8-sided polygon is called an octagon.


You can remember the prefix oct by thinking of an octopus l.jpg

You can remember the prefix “oct” by thinking of an octopus.


A 9 sided polygon is called a nonagon l.jpg

A 9-sided polygon is called a nonagon.


Slide33 l.jpg

You can remember that a nonagon has nine sides because the words nonagon and nine both have two “ns.”


A 10 sided polygon is called a decagon l.jpg

A 10-sided polygon is called a decagon.


You can remember the prefix dec by thinking about a decade l.jpg

You can remember the prefix “dec” by thinking about a decade.

2000

1999

1998

1997

1996

1995

TEN YEARS

1994

1993

1992

1991


Let s explore some interesting properties of polygons l.jpg

Let’s explore some interesting properties of polygons.


All triangles have a certain characteristic about them l.jpg

All triangles have a certain characteristic about them.


If you tear off the three corners of any triangle l.jpg

If you tear off the three corners of any triangle…


Slide39 l.jpg

If you tear off the three corners of any triangle…


Slide41 l.jpg

…you can arrange the three angles to form a semicircle.


Slide51 l.jpg

If a circle has 360, then ½ of a circle must have 180.


This property is true for any triangle l.jpg

This property is true for any triangle.


Now let s explore the sum of the 4 angles in any quadrilateral l.jpg

Now let’s explore the sum of the 4 angles in any quadrilateral.


Any convex quadrilateral can be split into 2 triangles l.jpg

Any convex quadrilateral can be split into 2 triangles.


If each triangle consists of 180 then 2 triangles would total 360 l.jpg

If each triangle consists of 180, then 2 triangles would total 360.

180

180


This can easily be seen in the square l.jpg

This can easily be seen in the square.

90 + 90 + 90 + 90 = 360

90

90

90

90


Any convex pentagon can be split into 3 triangles l.jpg

Any convex pentagon can be split into 3 triangles.


Each triangle consists of 180 l.jpg

Each triangle consists of 180.

180

180

180


Slide60 l.jpg

180 + 180 + 180 = 540

180

180

180


Now let s chart our findings l.jpg

Now let’s chart our findings.


Slide62 l.jpg

Do you notice any pattern?


Slide63 l.jpg

As the number of sides on the polygons increase by 1 side, the sum of the angles increases by 180.

+ 180

+ 180


What is the sum of all angles in a convex hexagon l.jpg

What is the sum of all angles in a convex hexagon?


Slide65 l.jpg

hexagon


Slide66 l.jpg

hexagon

720


Let s explore one more interesting characteristic about polygons l.jpg

Let’s explore one more interesting characteristic about polygons.


A diagonal in a polygon connects two vertices corners l.jpg

A diagonal in a polygon connects two vertices (corners).


A quadrilateral has 2 diagonals l.jpg

A quadrilateral has 2 diagonals.


A pentagon has 5 diagonals l.jpg

A pentagon has 5 diagonals.


A hexagon has 9 diagonals l.jpg

A hexagon has 9 diagonals.


How many diagonals are in a triangle l.jpg

How many diagonals are in a triangle?


That s a trick question a triangle has no diagonals l.jpg

That’s a trick question. A triangle has no diagonals.


Now let s chart our findings and look for a pattern l.jpg

Now let’s chart our findings and look for a pattern.


Slide75 l.jpg

Do you notice any pattern?


Slide76 l.jpg

Now let’s chart our findings and look for a pattern.

+ 2

+3

+4


This concludes our show on polygons l.jpg

This concludes our show on polygons.

The End.


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