Download CP Geometry Name: Lesson 6-1: Properties and Attributes of

CP Geometry
Name: _____________________________
Lesson 6-1: Properties and Attributes of Polygons Date: __________________ Block: ______
Recall, a ___________________ is a plane figure that meets the following conditions:
1. It is a closed figure formed by three or more coplanar segments called ______________.
2. Sides that have a common endpoint are ________________________________.
3. Each side intersects exactly two other sides, one at each endpoint, called a __________.
Diagonal: ________________________________________________________________________
________________________________________________________________________________
Polygons are either convex or concave. A polygon is convex if no diagonal contains points in the
__________________ of the polygon. A polygon is concave if any part of a ___________________
contains points in the exterior of the polygon.
Diagram:
Convex Polygon
Concave Polygon
Regular Polygon: __________________________________________________________________
Types of Polygons:
Number of
Sides
3
Name of Polygon
Number
of Sides
8
4
9
5
10
6
12
7
n
Name of Polygon
Example 1: Tell whether each figure is a polygon. If it is a polygon, name it by the number of sides.
a.
b.
c.
Example 2: Tell whether each polygon is regular or irregular. Tell whether it is concave or convex.
a.
b.
c.
**To find the sum of the interior angle measures of a convex polygon, draw all possible diagonals
from one vertex of the polygon. This creates a set of ______________________. The sum of the
angle measures of all the triangles equals the sum of the angle measures of the polygon.
Polygon
Number of
Sides
Number of
Triangles
Sum of Interior Angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
The sum of the measures of the interior angles of a convex polygon:
Example 3: Find each measure.
a. Find the sum of the interior angles of a convex heptagon.
b. Find the measure of each interior angle of a regular hexagon.
c. Find the measure of each interior angle of pentagon ABCDE.
Consider the following diagram of a convex polygon with its exterior angles shaded.
If we were to cut out the exterior angles we could slide them together at their vertices.
Notice that when they are brought together, the three exterior angles fit together perfectly all the
way around a point. How many degrees are there all the way around a point? ____________
The diagram can be extended to polygons with different numbers of sides.
The sum of the measures of the exterior angles of a convex polygon:
An interior and exterior angle of a polygon form a __________________________________.
Example 4: Find each measure.
a. Find the sum of the exterior angles of a convex dodecagon.
b. Find the measure of each exterior angle of a regular 20-gon.
c. Find the value of b in polygon FGHJKL.
Example 5: The aperture of the camera is formed by ten blades. The blades overlap to form a
regular decagon. What is the measure of  CBD?
Example 6: Ann is making paper stars for party decorations. What is the measure of 1?