U6 L3 Angle Relationships in Polygons...
Transcript of U6 L3 Angle Relationships in Polygons...
![Page 1: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/1.jpg)
U6 L3 Angle Relationships in Polygons complete.notebook
1
February 12, 2015
Warm Up:
80
25
![Page 2: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/2.jpg)
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.
![Page 3: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/3.jpg)
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.
![Page 4: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/4.jpg)
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
![Page 5: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/5.jpg)
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?
![Page 6: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/6.jpg)
U6 L3 Angle Relationships in Polygons complete.notebook
6
February 12, 2015
![Page 7: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/7.jpg)
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)
![Page 8: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/8.jpg)
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.
![Page 9: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/9.jpg)
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°?
![Page 10: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/10.jpg)
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
![Page 11: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/11.jpg)
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)
![Page 12: U6 L3 Angle Relationships in Polygons completeteachers.wrdsb.ca/dberry/files/2015/02/U6-L3-Angle... · 2017. 2. 18. · U6 L3 Angle Relationships in Polygons complete.notebook 2 February](https://reader033.fdocuments.us/reader033/viewer/2022060905/60a076868bc3396e0a605d7e/html5/thumbnails/12.jpg)
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