u6 l3 angle relationships in polygons...
TRANSCRIPT
U6 L3 Angle Relationships in Polygons complete.notebook
1
February 12, 2015
Warm Up:
80
25
U6 L3 Angle Relationships in Polygons complete.notebook
2
February 12, 2015
Geometric Relationships
Day 3: Angle Relationships in Polygons
Learning Goal:
Students can describe the proper�es and rela�onships of the interior
and exterior angles of any polygon.
U6 L3 Angle Relationships in Polygons complete.notebook
3
February 12, 2015
SOME MORE KEY TERMS:
Convex Polygon: a polygon where all interior angles are less than 180o.
Concave Polygon: a polygon where there is at least one interior angle
greater than 180o.
U6 L3 Angle Relationships in Polygons complete.notebook
4
February 12, 2015
0
18010
170 20
16030
150
40
140
50
130
60
120
70
110
80
100
90
90
152°
100
80
110
70
120
60
130
50
14040
150 30
16020
170
10
180
0
U6 L3 Angle Relationships in Polygons complete.notebook
5
February 12, 2015
How do the interior angles of the triangles relate to
the interior angles of the pentagon?
U6 L3 Angle Relationships in Polygons complete.notebook
6
February 12, 2015
U6 L3 Angle Relationships in Polygons complete.notebook
7
February 12, 2015
EXAMPLE 1. For the following Hexagon (6 sided figure), calculate the
sum of the interior and exterior angles.
Sum of the interior angles =
Sum of the exterior angles =
b) What formula could we come up with to find the sum of the
interior angles of any “n” sided polygon?
65
59
Sum of interior angles = 180(n - 2)
U6 L3 Angle Relationships in Polygons complete.notebook
8
February 12, 2015
of Sides
3 0 1 180 360
4 1 2 360 360
5 2 3 540 360
6
7
Octagon 8
EXAMPLE 2. Complete the following chart.
U6 L3 Angle Relationships in Polygons complete.notebook
9
February 12, 2015
EXAMPLE 3.
EXAMPLE 4. How many sides does a polygon have if the sum of its interior
angles is 1980°?
U6 L3 Angle Relationships in Polygons complete.notebook
10
February 12, 2015
EXAMPLE 5.
a) Draw a 10 sided polygon
b) Calculate how many diagonals you could draw from any one vertex of this
polygon.
c) Calculate the sum of the interior angles using 2 different methods
U6 L3 Angle Relationships in Polygons complete.notebook
11
February 12, 2015
Answer the following ques�on on a separate piece of paper.
When you are done, hand it in to Ms. Berry (don't forget your name).
EXIT CARD: Determine the measure of each interior angle of a regular
9 sided polygon. (Show your work)
RECALL: "regular" means that all the sides are the same
length (and consequently all the angles as well)
U6 L3 Angle Relationships in Polygons complete.notebook
12
February 12, 2015
Meet in the Computer Lab
Room 112
Practice: p. 391 #1-12, 14, 20