1. Exploring Polygons By the end of class you will be able to: Identify Convex and Concave Polygons Name Parts of a Polygon Classify Polygons

2. 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.)

3. Example 1: Which figures are polygons?

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

5. Example 1: Which figures are polygons? polygon

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

7. 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. VerticesInterior AnglesExterior Angles Perimeter Area Sides

8. 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         

9. 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. VerticesInterior Angles ) ) ) ) ) ) ) ) ) ) )

10. 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. VerticesInterior AnglesExterior Angles

11. 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. VerticesInterior AnglesExterior Angles Sides

12. 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. VerticesInterior AnglesExterior Angles Perimeter Add all sides Sides

13. 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. VerticesInterior AnglesExterior Angles Perimeter Area Sides

14. Parts of a polygon In more complex polygons there are more parts. Learn these new terms: DiagonalRegularConsecutive

15. Parts of a polygon In 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.) DiagonalRegularConsecutive ) )

16. Parts of a polygon In more complex polygons there are more parts. Learn these new terms: DiagonalRegularConsecutive Joins two nonconsecutive vertices. (Notice the triangle does NOT have any diagonals.)

17. Parts of a polygon In more complex polygons there are more parts. Learn these new terms: A polygon that is equilateral and equiangular. ) ) ) ) ) ) ) ) ) ) ) DiagonalRegularConsecutive

18. Classifying Polygons A Polygon is classified by its’ number of sides. 3 4 5 6 7 8 9 10 12 nn - gon Dodecagon Decagon Nonagon Octagon Heptagon Hexagon Pentagon Quadrilateral Triangle Number of SidesType of Polygon

19. Example: The perimeter of the pentagon is 20. Solve for X. X+12X 2X-1 X + 6 X Remember what perimeter means The Sum of all the sides

20. Example: The perimeter of the pentagon is 20. Solve for X. X+12X 2X-1 X + 6 X (X+ 1) + (2X) +(X) + (2x-1) + (x+6 )= 20 Combine like terms and solve 7X + 6 = 20 7 X = 14 X = 2