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Geometry
Polygons General Information
A polygon is a plane figure that meets two conditions:
1) It is formed by three or more _____________ called ____________, such that no two
________ with a common endpoint are _____________.
2) Each __________ intersects exactly two other sides, one at each endpoint, or
__________ (plural ______________).
Examples: Tell if the shape is a polygon or not. If it isn’t tell why.
1.
2.
3.
Polygons are names by the number of sides they have.
# of Name
Sides
3
4
5
6
7
# of
Sides
8
9
10
12
n
Name
4.
A polygon is ____________ if no line that contains a side of the polygon contains a
point in the interior of the polygon.
Example:
You draw one:
A polygon that is not convex is called ______________ or _______________/
Example:
You draw one:
Examples: Decide if the polygon is convex or concave. Then name the polygon by
the number of sides it has.
1.
2.
3.
4.
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A polygon is _______________________ if all of its sides are congruent.
A polygon is ________________ if all of its interior and exterior angles are
congruent.
A polygon is ___________________ if it is both of these.
Examples: Determine if the polygon is any of the above.
5.
6.
7.
Polygon Interior Angles Theorem
The ___________of the measures of the _________________ angles of a
convex polygon is ______________________.
m  1  m  2  m  3  m  4  m  5  m  6  (n  2) 180
Examples:
1. Find the sum of the measure of the interior angles of a convex decagon.
2. The sum of the measures of the interior angles of a convex polygon is 2340 . Classify
the polygon by the number of sides.
Find the value of x .
3.
4.
Polygon Exterior Angles Theorem
The ___________of the measures of the _________________ angles of a
convex polygon is ______________________.
m  1  m  2  m  3  m  4  m  5  360
Examples:
5. A convex hexagon has exterior angles with measures 34 , 49 , 58 , 67 , and 75 . What
is the measure of an exterior angle at the sixth vertex?
6. A trampoline is shaped like a regular dodecagon.
a. Find the measure of each interior angle.
b. Find the measure of each exterior angle.
7. Find the value of x