1. Warm Up 1. How many sides do the following figures have? b) a)
2. Solve for x. 50
2x - 12 b) a) 35
2x + 7

2. Section 1.6 Classifying Polygons

3. A Polygon is a closed plane figure with the following properties:
What is a Polygon?
A Polygon is a closed plane figure with the following properties:
1) Is formed by 3 or more line segments (sides)
2) Each side intersects exactly 2 sides, but only at their endpoints

4. 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.)

5. convex concave A Polygon can either be convex or concave.
no sides go through the interior of the polygon.
convex
concave
A side goes through the interior of the polygon.

6. Which figures are polygons?
Example 1:
Which figures are polygons?

7. Which figures are polygons?
Example 1:
Which figures are polygons?
polygon
polygon
polygon
polygon

8. Label the polygons as convex or concave?
Example 2:
Label the polygons as convex or concave?

9. Label the polygons as convex or concave?
Example 2:
Label the polygons as convex or concave?
convex
concave
concave
convex

10. Parts of a polygon Vertices Interior Angles Exterior Angles Area Sides
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

11. Parts of a polygon           
Vertices – each endpoint of a side           

12. Parts of a polygon
Interior Angles ) )

13. Parts of a polygon
Exterior Angles

14. Parts of a polygon
Sides

15. Parts of a polygon
Perimeter
Add all sides

16. Amount of surface covered by a figure
Parts of a polygon
Area
Amount of surface covered by a figure

17. In more complex polygons there are more parts. Learn these new terms:
Parts of a polygon
In more complex polygons there are more parts.
Learn these new terms:
Consecutive
Diagonal
Regular

18. Parts of a polygon Consecutive (side/angles)
Refers to parts that are right next to each other.
(They share a common vertex or side.) )

19. Parts of a polygon Diagonal
A segment that joins two nonconsecutive vertices.
(Notice the triangle does NOT have any diagonals.)

20. A convex polygon that is equilateral and equiangular.
Parts of a polygon
Regular
A convex polygon that is equilateral and equiangular. ) )

21. A Polygon is classified by its’ number of sides.
Type of Polygon 12 n 9 10 4 3 8 5 6 7
Pentagon
Quadrilateral
Hexagon
Triangle
n - gon
Dodecagon
Decagon
Nonagon
Octagon
Heptagon

22. A Polygon is classified by its’ number of sides.3 4 5 10 7 8 9 6 11
n-gon : can be used to name a polygon
n = number of side
ex: 100-gon
-refers to a polygon with 100 sides
What do you notice as n gets bigger?

23. Examples
Name each polygon by its number of sides. Then classify it as convex or concave and equilateral, equiangular, or regular. 4 )

24. Tell Whether the statement is always, sometimes, or never true.
Examples
Tell Whether the statement is always, sometimes, or never true.
A regular polygon is equiangular.
A triangle is convex.
A regular polygon is equilateral.

25. Example
The expression (-2x + 41) and (7x - 40) represent the lengths of two sides of a equilateral pentagon. Find the side of the pentagon.

26. Example
The expression (9x + 5) and (11x - 25) represent the measures of two angles of a regular nonagon. Find the measure of angle of the nonagon.

27. Homework Workbook p16 #’s 1-23 odd