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8.1 Exploring Polygons
Created by:
Cathy and Jim Carroll
Convex and Concave Polygons
Parts of a Polygon
Regular Polygons
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, when extended, pass through the interior of
the polygon. (All vertices point outside the polygon.)
A polygon is concave when a side that is extended
passes 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 polygonThe 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
Perimeter AreaSides
Parts of a polygonThe 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
Parts of a polygonThe 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
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Parts of a polygonThe 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 polygonThe 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 polygonThe 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
Perimeter
Add all sides
Sides
Parts of a polygonThe 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
Perimeter AreaSides
Parts of a polygonIn more complex polygons there are more parts.
Learn these new terms:
Diagonal RegularConsecutive
Parts of a polygonIn more complex polygons there are more parts.
Learn these new terms:
Refers to parts that are right next to each other.
(They share a common vertex or side.)
Diagonal RegularConsecutive
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Parts of a polygonIn more complex polygons there are more parts.
Learn these new terms:
Diagonal RegularConsecutive
Joins two nonconsecutive vertices.
(Notice the triangle does NOT have any diagonals.)
Parts of a polygonIn more complex polygons there are more parts.
Learn these new terms:
A polygon that is equilateral and equiangular.)
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Diagonal RegularConsecutive
Example 3: Identifying and Classifying Regular Polygons
Name each polygon and tell whether it is aregular polygon. If it is not, explain why not.
The figure is a regularquadrilateral. A regular quadrilateral is also called a square.
The figure is aquadrilateral. It is not a regular polygon becauseall of the sides are not congruent.
A. B.
Course 2
Now You Try…
Insert Lesson Title Here
The figure is a triangle. It is not a regular polygon because all sides and angles are not congruent.
The figure is a regular triangle.
Name each polygon and tell whether it is aregular polygon. If it is not, explain why not.
A. B.
Course 2
Is the figure convex or concave?
A.ConvexB.Concave
Is the figure convex or concave?
A.ConvexB.Concave
Is the figure convex or concave?
A.ConvexB.Concave
Decide whether the figure is equilateral, equiangular, or neither.
A. Equilateral B. Equiangular C. Neither
Decide whether the figure is equilateral, equiangular, or neither.
A. Equilateral B. Equiangular C. Neither
Decide whether the figure is equilateral, equiangular, or neither.
A. Equilateral B. Equiangular C. Neither
True or FalseThe figure is regular.
TRUE
True or FalseThe figure is regular.
FALSE
True or FalseThe figure is regular.
TRUE
The below figure is regular.Find the value of x.
x = 5
The below figure is regular.Find the value of x.
x = 36
The below figure is regular.Find the value of x.
x = 7
