Transcript Polygon - MartinMathSite1

6.1 Exploring Polygons
•Convex and Concave
Polygons
•Parts of a Polygon
•Classifying Polygons
Created by Cathy and Jim Carroll
Convex or Concave?
A Polygon is a plane figure formed by three or
more segments.
A Polygon can either be convex or concave.
If a polygon is convex then no sides go
through the interior of the polygon.
(All vertices point outside the polygon.)
If a polygon is concave then it is not convex. A
side goes through the interior of the polygon.
(At least one vertex points inside the polygon.)
Example 1:
Which figures are polygons?
Example 1:
Which figures are polygons?
polygon
polygon
polygon
polygon
Example 2:
Label the polygons as convex or concave?
Example 2:
Label the polygons as convex or concave?
convex
concave
concave
convex
Parts of a polygon
The simplest polygon is a triangle. Many of the
terms you learned about a triangle apply to all
polygons. Remind yourself of what the following
terms mean.
Vertices
Interior Angles
Exterior Angles
Area
Sides
Perimeter
Parts of a polygon
The simplest polygon is a triangle. Many of the
terms you learned about a triangle apply to all
polygons. Remind yourself of what the following
terms mean.
Vertices
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
Parts of a polygon
The simplest polygon is a triangle. Many of the
terms you learned about a triangle apply to all
polygons. Remind yourself of what the following
terms mean.
Vertices
Interior Angles
Parts of a polygon
The simplest polygon is a triangle. Many of the
terms you learned about a triangle apply to all
polygons. Remind yourself of what the following
terms mean.
Vertices
Interior Angles
Exterior Angles
Parts of a polygon
The simplest polygon is a triangle. Many of the
terms you learned about a triangle apply to all
polygons. Remind yourself of what the following
terms mean.
Vertices
Interior Angles
Exterior Angles
Sides
Parts of a polygon
The simplest polygon is a triangle. Many of the
terms you learned about a triangle apply to all
polygons. Remind yourself of what the following
terms mean.
Vertices
Interior Angles
Exterior Angles
Sides
Perimeter
Add all sides
Parts of a polygon
The simplest polygon is a triangle. Many of the
terms you learned about a triangle apply to all
polygons. Remind yourself of what the following
terms mean.
Vertices
Interior Angles
Exterior Angles
Area
Sides
Perimeter
Parts of a polygon
In more complex polygons there are more parts.
Learn these new terms:
Consecutive
Diagonal
Regular
Parts of a polygon
In more complex polygons there are more parts.
Learn these new terms:
Consecutive
Diagonal
Regular
Refers to parts that are right next to each other.
(They share a common vertex or side.)
Parts of a polygon
In more complex polygons there are more parts.
Learn these new terms:
Consecutive
Diagonal
Regular
Joins two nonconsecutive vertices.
(Notice the triangle does NOT have any
diagonals.)
Parts of a polygon
In more complex polygons there are more parts.
Learn these new terms:
Consecutive
Diagonal
Regular
A polygon that is equilateral and equiangular.
Classifying Polygons
A Polygon is classified by its’ number of sides.
Number of Sides
Type of Polygon
3
4
5
6
7
8
9
10
12
n
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n - gon
Example:
The perimeter of the pentagon is 20. Solve for X.
X+1
Remember what
perimeter means
2X
X
2X-1
X+6
The Sum of all the sides
Example:
The perimeter of the pentagon is 20. Solve for X.
X+1
X
Combine like
terms and solve
2X
2X-1
X+6
(X+ 1) + (2X) +(X) + (2x-1) + (x+6 )= 20
7X + 6 = 20
7 X = 14
X=2