Geo1.4 Polygons Lesson
Transcript of Geo1.4 Polygons Lesson
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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
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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:
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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?
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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
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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
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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.
_ _ _ _
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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.
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How many diagonals do I have?
• Identify how many diagonals does polygon CRAZY have…
Z
Y
C
R
A
5 diagonals
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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
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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!!
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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!
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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!
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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!
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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?
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YES… WE CAN!!!
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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.