Download Chapter 3.4 Polygons Day 1.notebook

Chapter 3.4 Polygons Day 1.notebook
February 07, 2013
Polygon­ A closed plane figure with at least 3 sides that are segments. The sides intersect only at their endpoints and no adjacent sides are collinear.
3.4 The Polygon Angle­Sum Theorems
Objective: To classify polygons
To find the sums of the measures of the interior and exterior angles of polygons
M.2.B.
Performance Standard 3.6 DOK­1
Knowledge MA 3
counter­example:
examples:
Aug 4­6:47 AM
Aug 4­6:48 AM
Polygons
Diagonals: a segment drawn from one vertex to any other non­
consecutive vertex
# of sides
type
3
4
5
6
7
Convex: when all diagonals lie on the insode of the polygon
8
9
10
n
Aug 4­6:52 AM
Concave: when any part of the diagonals fall on the outside of the polygon.
Aug 4­7:00 AM
Naming a polygon­ Start at any vertex and list vertices consecutively.
A
L
R
B
G
E
List the vertices:
List the sides:
List the angles:
Name: ALGEBR Hmmmmmm ... Can a triangle be convex? Concave??? Why??
Aug 4­7:02 AM
Aug 4­7:46 AM
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Chapter 3.4 Polygons Day 1.notebook
February 07, 2013
Classify the polygon. Use three words if possible.
Ex 1)
Ex 2)
Ex 3)
Ex 4)
Remember equiangular?? What about equilateral?
When a polygon is both equiangular AND equilateral, we call it REGULAR.
Aug 4­7:05 AM
Aug 4­7:10 AM
Classify the polygon. Use three words if possible.
Sketch the polygon if possible.
Ex 6)
Ex 5)
Ex 8) Regular hexagon
Ex 9) Equilateral right triangle
Ex 7)
70
70
Ex 10) Concave equiangular qualdrilateral
Aug 4­7:13 AM
Aug 4­7:18 AM
Exploration: Triangles and polygons
Using the dot paper provided, work with your desk partner and sketch each polygon.
Fill out the chart on your paper.
Type of
polygon
# of sides
# of triangles
Sum of the interior angles
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
Aug 4­7:30 AM
Aug 4­7:31 AM
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Chapter 3.4 Polygons Day 1.notebook
February 07, 2013
What conjectures can you make about the relationship between the number of sides of a polygon and the sum of the interior angles (1st and 4th column)? (Hint: think about patterns)
Aug 4­7:41 AM
Feb 7­12:20 PM
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