1. Classifying Polygons
Section 8.1

2. Objectives
Describe polygons.

3. Key Vocabulary Concave Convex Equilateral polygon Equiangular polygon
Regular polygon

4. Polygons
Polygon – a closed figure whose sides are formed by a finite number of coplanar segments called sides.
the sides that have a common endpoint are noncollinear
each side intersects exactly two other sides, but only at their endpoints.
The vertex of each angle is a vertex of the polygon. A polygon is named by using the letters of its vertices, written in consecutive order.

5. Polygons - Examples

6. Types of Polygons
If the lines of any segment of the polygon are drawn and any of the lines contain points that lie in the interior of the polygon, then it is concave.
Otherwise, it is convex (no points of the lines are in the interior).

7. Classifying Polygons
Polygons are classified by the number of sides they have. A polygon with n number of sides is an n-gon.
Polygon Number of Sides
Triangle 3
Quadrilateral
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Hendecagon 11
Dodecagon 12

8. More Classifying Polygons
An equilateral polygon is a polygon in which all sides are congruent.
An equiangular polygon is a polygon in which all angles are congruent.

9. Regular Polygons
A convex polygon in which all of the sides and all of the angles are congruent is called a regular polygon.
An irregular polygon is a polygon that is not regular.
Regular Polygons

10. Example Regular Polygon?( ) ( ) ( )) ( ((
yes
NO!
NO!

11. Decide whether the polygon is convex or concave.
Example 1
Identify Convex and Concave Polygons
Decide whether the polygon is convex or concave. a. b.
SOLUTION a.
At least one extended side passes through the interior. So, the polygon is concave. b.
None of the extended sides pass through the interior. So, the polygon is convex. 11

12. Decide whether the polygon is regular. Explain your answer.
Example 2
Identify Regular Polygons
Decide whether the polygon is regular. Explain your answer. a. b. c.
SOLUTION
Although the polygon is equiangular, it is not equilateral. So, the polygon is not regular. a.
Because the polygon is both equilateral and equiangular, it is regular. b.
Although the polygon is equilateral, it is not equiangular. So, the polygon is not regular. c. 12

13. Your Turn:
Decide whether the polygon is convex or concave. Then decide whether the polygon is regular. Explain your answer.
ANSWER
convex; not regular (equilateral but not equiangular) 1.
ANSWER
concave; not regular (equilateral but not equiangular) 2.
ANSWER
convex; regular (both equilateral
and equiangular) 3.

14. Example 3a:
Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular.
There are 4 sides, so this is a quadrilateral.
No line containing any of the sides will pass through the interior of the quadrilateral, so it is convex.
The sides are not congruent, so it is irregular.
Answer: quadrilateral, convex, irregular

15. Example 3b:
Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular.
There are 9 sides, so this is a nonagon.
A line containing some of the sides will pass through the interior of the nonagon, so it is concave.
The sides are not congruent, so it is irregular.
Answer: nonagon, concave, irregular

16. Your Turn:
Name each polygon by the number of sides. Then classify it as convex or concave, regular or irregular. a. b.
Answer: triangle, convex, regular
Answer: quadrilateral, convex, irregular

17. Assignment
Pg. 413 – 415: #3 – 43 odd