1. Teacher will introduce Polygons:
 Definition: closed many-sided geometric figure
 Properties:
o Each segment intersects two others each at an end point
o Each vertex has exactly 2 line segments coming out of it
o Regular polygon: each angle has same measure and each line
segment is of equal length
2. Students will fill in left column in table of polygons:
Polygon
Number of Sides
Regular Polygon
(all angles are equal and length of all sides are
equal)
3
Equilateral Triangle
Triangle
4
Square
Quadrilateral
5
Pentagon
Regular Pentagon
6
Hexagon
Regular Hexagon
7
Heptagon
Regular Heptagon
8
Octagon
Regular Octagon
10
Decagon
Regular Decagon
12
Dodecagon
Regular Dodecagon
3. Explain drawing diagonals in a polygon:
 Definition of a Diagonal – Two parts
1. Line formed by connecting 2 vertices of a polygon which is
not already a side
2. Want is so one diagonal does not cross another diagonal
4. Teacher will show that drawing diagonals leads to triangles:
Leads to just drawing all the diagonals that come out of one vertex
o No matter what vertex you start at, you will end with the same
number of triangles
o Show pattern for: number of triangles = (# of sides – 2)
Number of sides for the
polygon = n
Number of triangles formed
by diagonals from 1 vertex
Difference between number
of sides and number of
triangles
4
5
6
:
:
2
3
4
4–2=2
5–3=2
6–4=2
n
n-2
n – (n – 2) = 2
5. Teacher reminds students that the sum of the angles of a triangle is
always 180 degrees
 Therefore,
(# triangles in a certain polygon)*(180 degrees) = sum of angles in
that polygon
or since: (# of triangles) = (# of sides – 2)
(# of sides – 2)*(180 degrees) = sum of all angles of n-gon
6. Students will then get into groups and fill in the table given below:
Polygon: n =
number of
sides
3
4
5
6
7
8
9
10
50
100
Number of
diagonals
from each
vertex
(n - 3)
Number of
triangles
possible
(n – 2)
Total
number of
degrees in
polygon
(n – 2)*180
Can you find a relationship
between the names of the
polygons and a common
name or event? (sports,
animals, science, buildings,
etc.) Try to come up with
at least 2 examples.
Answers: Relate prefixes to sports: triathlon, decathlon or certain chemicals: octane,
pentane, pentagon (building) quadriplegic, octopus, etc.
During this portion of the lesson, the teachers will walk around and “coach elaborate”
with the students asking questions such as:

Why do you think the number of triangles will be the same no matter what vertex
you start with?
 Why do you think the number of triangles is always three less than the number of
sides?
 Why can’t diagonals intersect?
 Why is a triangle the smallest possible polygon?
 If you start with a triangle and find all the answers, what will happen to the
answers when you add one side and start with a quadrilateral? What if you add 5
sides?
 Why do we use triangles to find the angle sum?
The teacher will make sure that each student in the group answers at least one question to
get a more general idea of what the class knows as a whole.
6. Teachers will lead a whole class discussion where the groups will tell the class what
they got as answers for the table and for the question asked.