Polygons – Guided Notes
Vocabulary
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Congruent:
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Adjacent:
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Opposite:
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Parallel:
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Perpendicular:
Polygons
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Polygon:
Draw a picture of a polygon

Draw a picture of a shape that is not a polygon
Regular Polygon:
Draw a picture of a regular polygon
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Convex:

Concave:
Draw a picture of a convex polygon
Draw a picture of a not regular (irregular) polygon
Draw a picture of a concave polygon
Triangles:

Right Triangle:
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Scalene Triangle:

Isosceles Triangle:
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Equilateral Triangle:
Draw and label a picture of each type of triangle
Quadrilateral:
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Parallelogram:
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Rectangle:
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Rhombus:
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Square:

Trapezoid:
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Kite:
Draw and label a picture of each type of quadrilateral
Other polygons
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Pentagon:
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Hexagon:
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Heptagon:
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Octagon:
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Nonagon:
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Decagon:
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N – gon:
Draw and label a picture of each type of polygon
Interior angles of polygons

The sum of the interior angles of a triangle is:
From a single vertex (corner), how many triangles can be made from the following quadrilateral?

The sum of the interior angles of a quadrilateral is:
Draw the shapes for the polygons with the following number of sides and complete the table
Number of
sides
Number of
triangles
Sum of interior
angles
3
4
5
6
7
8
9
Using the data in your table write the equation for the sum of interior angles of a polygon with (n) sides
𝑆𝑢𝑚 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒𝑠 𝑜𝑓 𝑎 𝑝𝑜𝑙𝑦𝑔𝑜𝑛 =

What is the sum of the interior angles for a 22 – sided shape?
Remember your definition of a regular polygon. What is the equation for the measure of 1 interior angle of a
polygon?
𝑀𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑎 𝑠𝑖𝑛𝑔𝑙𝑒 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑎 𝑝𝑜𝑙𝑦𝑔𝑜𝑛 =

What is the sum of the interior angles of a regular pentagon?

What is a measure of one of the interior angles?
Exterior angles of a polygon
By extending each side of a polygon (see below figure) you can create an exterior angle at each vertex

Assume that both shapes are
regular. Find the measure of each
interior angle in the two polygons.
Triangle =
Pentagon =

Using the fact that the angle sum of a straight line is 180 degrees. Find the measure each exterior
angle in the triangle and the pentagon. Then find the measure of the sum of exterior angles for each
polygon
Triangle
Pentagon
Each exterior angle =
Each exterior angle =
The sum of exterior angles =
The sum of exterior angles =

Using the pattern you found above. What is the sum of exterior angles for any regular polygon?

What is the equation for finding a single exterior angle for a regular polygon?
Example problem
a) What is the measure of an interior angle of a regular hexagon?
b) What is the measure of an exterior angle of a regular hexagon?
c) What is the sum of interior angles for a regular 15 – gon?
d) What is the sum of exterior angles for a regular 32 – gon?