1. Objectives Classify polygons based on their sides and angles.
Find and use the measures of interior and exterior angles of polygons.

2. Each segment that forms a polygon is a side of the polygon
Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.

3. You can name a polygon by the number of its sides
You can name a polygon by the number of its sides. The table shows the names of some common polygons.

4. A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints.
Remember!

5. Example 1A: Identifying Polygons
Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.
polygon, hexagon

6. Example 1B: Identifying Polygons
Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.
polygon, heptagon

7. Example 1C: Identifying Polygons
Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.
not a polygon, curved sides

8. Check It Out! Example 1a
Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.
not a polygon, not closed

9. Check It Out! Example 1b
Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides.
polygon, nonagon

10. Check It Out! Example 1c
Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides.
not a polygon, curved side

11. Check It Out! Example 1d
Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides.
not a polygon, sides cross

12. All the sides are congruent in an equilateral polygon.
All the angles are congruent in an equiangular polygon.
A regular polygon is one that is both equilateral and equiangular.
If a polygon is not regular, it is called irregular.

13. A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex.

14. Example 2A: Classifying Polygons
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
irregular, convex

15. Example 2B: Classifying Polygons
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
irregular, concave

16. Example 2C: Classifying Polygons
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
regular, convex

17. Check It Out! Example 2a
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
regular, convex

18. Check It Out! Example 2b
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
irregular, concave

19. Pratice Quiz
1. Name the polygon by the number of its sides. Then tell whether the polygon is regular or irregular, concave or convex.
nonagon; irregular; concave

20. Jokes
Why can't your nose be 12 inches long?
Because then it would be a foot!
How do you cure a headache?
Put your head through a window and the pane will just disappear!