Polygons
Goals:
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Method used to find the total number of degrees in any polygon
Method used to find number of degrees in one angle of a regular polygon
Method used to find number of degrees in one exterior angle of a polygon
Each person gets a shape. You are a team so benefit from your teammates shapes, too.
From one vertex only draw all the diagonals that form triangles. Each
triangle is 180o. How many sides in your polygon? How many triangles? How
many degrees? Compare with your teammates.
Now draw a not regular polygon with the same number of sides as your
regular shape. Draw in the triangles from one vertex. Is there the same
number of triangles? Can you establish a relationship? How can you
determine the total number of degrees in a polygon?
If the shape is a regular polygon, how do you find the number of degrees in
one of its angles?
Draw the exterior angles of your polygons – both the regular and the not
regular. Have one exterior angle at each vertex. What is the relationship
between the interior and exterior angles? Now cut out the exterior angles
being careful to be sure what is the vertex of the angle. Arrange the angles
adjacent to each other with the vertices all meeting at one point. Look at
your teammates polygons. What conclusion can you make about the exterior
angles of a polygon?
Decagon has _____ sides (number)
A decagon has ____________ o (total degrees)
An interior angle of a regular decagon has ________ o (degrees)
An exterior angle of a regular decagon has ________ o (degrees)
Can you do this for a polygon of n sides?
POLYGON
GOALS:



Method used to find the total number of degrees in any polygon.
Method used to find number of degrees in one angle of a regular polygon.
Method used to find number of degrees in one exterior angle of a polygon.
You are a team, so work together. However, each student is ultimately responsible for one polygon
.
FIRST:
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From one vertex only draw all the diagonals that form triangles. You know
that each triangle is 180o.
How many sides does your polygon have? __________
How many triangles did you create? __________
How many degrees in total for the triangles? __________
Compare your results with your teammates' results.
SECOND:
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Now draw a not regular polygon with the same number of sides as your
regular shape.
Again, draw in the triangles from one vertex.
Are there the same number of triangles? __________
Can you establish a relationship?
_________
How can you determine the total number of degrees in a polygon?
THIRD:
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If the shape is a regular polygon, how do you find the number of degrees in
one of its angles?
_______________________________________________________
FOURTH:
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Draw the exterior angles of your polygons – both the regular and the not
regular. There will be one exterior angle at each vertex.
What is the relationship between the interior and exterior
angles? __________
Now cut out the exterior angles being careful to be sure what is the vertex
of the angle.
Arrange the angles adjacent to each other with the vertices all meeting at
one point.
Look at your teammates polygons.
What conclusion can you make about the exterior angles of a polygon?
__________________________________________________________
Decagon has _____ sides (number)
A decagon has ____________ o (total degrees)
An interior angle of a regular decagon has ________ o (degrees)
An exterior angle of a regular decagon has ________ o (degrees)
Can you do this for a polygon of n sides?