6.1--Properties & Attributes of Polygons Polygons are shapes that ...

6.1--Properties & Attributes of Polygons
Polygons are shapes that...
-are two dimensional (flat).
-are closed.
-have no holes or overlapping parts.
-don't cross themselves.
6.1--Properties & Attributes of Polygons
Are the following figures polygons or not?
1) 2)
3) 4)

6.1--Properties & Attributes of Polygons
Are the following figures polygons or not?
5) 6)
7)
6.1--Properties & Attributes of Polygons
Concave
Convex
Regular
-All sides congruent
-All angles congruent
Not Regular
-Everything else !!!

6.1--Properties & Attributes of Polygons
# of Sides
Name of Polygon
Interior Angle Sum
3
4
5
6
7
8
9
10
11
12
6.1--Properties & Attributes of Polygons
8) Give the technical name for each polygon pictured:
regular
convex
octagon
not regular
convex
pentagon

6.1--Properties & Attributes of Polygons
9) Give the technical name for each polygon pictured:
not regular
concave
decagon
regular
convex
pentagon
6.1--Properties & Attributes of Polygons
Theorem 6-1-1
(Polygon Angle Sum Theorem)
Interior Angle Sum = (n-2)(180)
Theorem 6-1-2
(Polygon Exterior Angle Sum Theorem)
Exterior Angle Sum = 360

6.1--Properties & Attributes of Polygons
Find the value of x:
10) 11)
89 o
127 o
(x+22) o
118 o
99 o (x+5) o (x+13) o
113 o
x o
130 o 123 o
6.1--Properties & Attributes of Polygons
Find the value of x:
12) 13)
x
x
x
x
x
(3x+10) o
x
x
x
x
81 o
95 o 72 o

6.1--Properties & Attributes of Polygons
14) Find the sum of the measures of the interior angles
of a convex 57-gon:
6.1--Properties & Attributes of Polygons
15) The sum of the measures of the interior angles of a
convex polygon is 3420 o . How many sides does it have?

6.1--Properties & Attributes of Polygons
16) Each of the exterior angles of a regular convex polygon
measures 72 o . How many sides does it have?
6.1--Properties & Attributes of Polygons
17) Each of the interior angles of a regular convex polygon
is five times larger than each of its exterior angles.
How many sides does the polygon have?