AIM 1.4: How can we define and classify polygons

with 3 to 12 sides?

DO NOW (4 minutes)◦ Using our knowledge of a ‘good’ definition, come up with

definitions for the following shapes:

1) Triangle2)Square3)Rectangle

REMINDER!Quiz #1 on MONDAY!

September 9th, 2009

Polygons

• What are polygons?– A polygon is a closed figure in a plane, formed by

connecting line segments endpoint to endpoint with each segment intersecting exactly two others.Polygons: NOT Polygons:

Sides & Vertices

• Each polygon has sides and vertices.– Sides are made up of the line segments on the polygon.– The point in which two sides meet is called a vertex.

side

side

vertex

vertex

How many sides and vertices does this

polygon have?

How do we notate polygons?• The following polygon needs a name!!

– What can you call it?

– We name a polygon by listing the vertices in consecutive order.

M

A

TH

•Polygon MATH

•Polygon ATHM•Polygon THMA•Polygon HMAT•Polygon MHTA•Polygon HTAM•Polygon TAMH•Polygon AMHT

Give me a name!

• Find up to four different ways you can name this polygon:

Z

Y

C

R

APolygon CRAZYPolygon RAZYCPolygon AZYCRPolygon ZYCRAPolygon YCRAZPolygon CYZARPolygon YZARCPolygon ZARCYPolygon ARCYZPolygon RCYZA

Let’s analyze this polygon!

consecutive sides

consecutive vertices

consecutive angles

Quadrilateral ABCDQuadrilateral ABCD1) What is this polygon’s name?

2) How many sides and vertices are there? 4 sides & 4 vertices4 sides & 4 vertices

3) Name all of my sides using proper notation. AB, BC, CD, and DAAB, BC, CD, and DA

4) Name all of my angles using proper notation. <ADC, < DCB, < CBA, <BAD<ADC, < DCB, < CBA, <BAD

5) Identify my consecutive sides.

6) Identify my consecutive vertices.

7) Identify my consecutive angles.

_ _ _ _

Diagonals• A diagonal of a polygon is a line segment that

connects two non-consecutive vertices.

Polygon ABCD has two diagonals. Polygon EFIHG has five diagonals.

This polygon is CONVEX. This polygon is CONCAVE because one or more diagonals are outside.

How many diagonals do I have?

• Identify how many diagonals does polygon CRAZY have…

Z

Y

C

R

A

5 diagonals

Classifying Polygons

• Polygons can be classified by the number of sides it has.

• We use Greek and Latin pre-fixes to name specific polygons.

• For example:

Triangle

Classifying PolygonsPolygon Name # of Sides # of Diagonals Drawing

Triangle 3

Quadrilateral 4

5

6

7

8

9

10

Undecagon 11

Dodecagon 12

n

In your notes, create this chart to act as a

guide to naming polygons.

Make sure you include space for the drawings.

Draw each polygon with the correct number of sides. Then, find the

number of diagonals up to the 6-sided polygon.

Try the others as a challenge!!

PolygonsPolygon Name # of Sides # of Diagonals

Triangle 3 0

Quadrilateral 4 2

Pentagon 5 5

Hexagon 6 9

Heptagon 7 14

Octagon 8 20

Nonagon 9 27

Decagon 10 35

Undecagon 11 44

Dodecagon 12 54

n-gon n ½n(n–3)

An Australian 50-cent coin is a dodecagon!

The UK 50-pence coin is a

heptagon!

Don’t forget to draw the polygons!

Quick Check!

• Draw a pentagon house with a quadrilateral chimney, three triangular windows, and a hexagonal sun.

• Include additional polygons for extra brownie points!!

GO!

Ever wonder…?

Ever wonder what a 38-gon is actually called?◦ A 38-sided polygon is called triacontakaioctagon!

How about a 100-gon?◦ A 100-sided polygon is called hectogon.

Find out more: http://mathforum.org/dr.math/faq/faq.polygon.names.html Go impress your friends!

Let’s try to say that one together!

Guided Practice

• Turn to pages 56-57. Work on #1 – 12.

I’m the polygon robot!

I’m the polygon robot!

What type of polygons is the robot made up of?

YES… WE CAN!!!

In closing…How do we classify and define polygons?How do you find the number of diagonals in a

polygon?

LOOKING AHEAD…◦ Tomorrow, we will take a deeper look at 3-sided

polygons, or triangles.

HOMEWORK…◦ Complete worksheet.