Download Unit 9 Day 1 Notes: Polygons - tperry-math

Unit 9 Day 1 Notes: Polygons
Definition of a polygonA polygon is a closed plane figure formed by three or more line segments.
Examples of figures that are NOT polygons:
Convex vs. Concave
A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no
diagonal contains points in the exterior, then the polygon is convex.
Concave polygons
Convex polygons
Names of polygons based on the NUMBER of sides
3-
7-
12-
4-
8-
13-
5-
9-
25-
6-
10-
n-
Regular polygon
A regular polygon has all sides congruent and all angles congruent. If a polygon is not regular,
then it is irregular.
Examples of regular polygons:
Interior (INT) angles vs. Exterior (EXT) angles
Diagonals and polygons (and patterns)
Shape
Num. Of
Sides
Num. Of
Triangles
Sum of
INT
Angles
Measure
of 1 INT.
Angle
Sum of
EXT.
Angles
Measure
of 1 EXT.
Angle
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
n-gon
In SUMMARY, FORMULAS (for CONVEX polygons):
Sum of the INTERIOR angles of a polygon with n sides:
Sum of the EXTERIOR angles of a polygon with n sides:
One INTERIOR angle of a regular polygon with n sides
One EXTERIOR angle of a regular polygon with n sides
Examples:
1. Find the sum of the measures of the interior angles of a convex 17-gon.
2. Find the measure of 1 interior angle of a regular 32-gon.
3. Find the sum of the measures of the exterior angles of a 27-gon.
4. Find the measure of 1 exterior angle of a regular 16-gon.
5. How many sides does a polygon have if the sum of the measures of the interior
angles is 5580 degrees?
6. How many sides does a regular polygon have if 1 interior angle has a measure of
162 degrees?
7. How many sides does a regular polygon have if 1 exterior angle has a measure of
5.625 degrees?