1. Holt Geometry 6-1 Properties and Attributes of Polygons 6-1 Properties and Attributes of Polygons Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2. Holt Geometry 6-1 Properties and Attributes of Polygons Warm Up 1. A ? is a three-sided polygon. 2. A ? is a four-sided polygon. Evaluate each expression for n = 6. 3. (n – 4) 12 4. (n – 3) 90 Solve for a. 5. 12a + 4a + 9a = 100 triangle quadrilateral 24 270 4

3. Holt Geometry 6-1 Properties and Attributes of Polygons Classify polygons based on their sides and angles. Find and use the measures of interior angles of polygons. Objectives

4. Holt Geometry 6-1 Properties and Attributes of Polygons side of a polygon vertex of a polygon diagonal regular polygon concave convex Vocabulary

5. Holt Geometry 6-1 Properties and Attributes of Polygons 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. Note 41

6. Holt Geometry 6-1 Properties and Attributes of Polygons You can name a polygon by the number of its sides. The table shows the names of some common polygons.

7. Holt Geometry 6-1 Properties and Attributes of Polygons A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints. Remember!

8. Holt Geometry 6-1 Properties and Attributes of Polygons 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

9. Holt Geometry 6-1 Properties and Attributes of Polygons 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

10. Holt Geometry 6-1 Properties and Attributes of Polygons 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

11. Holt Geometry 6-1 Properties and Attributes of Polygons 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

12. Holt Geometry 6-1 Properties and Attributes of Polygons 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

13. Holt Geometry 6-1 Properties and Attributes of Polygons 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

14. Holt Geometry 6-1 Properties and Attributes of Polygons 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.

15. Holt Geometry 6-1 Properties and Attributes of Polygons 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.

16. Holt Geometry 6-1 Properties and Attributes of Polygons Example 2A: Classifying Polygons Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, convex

17. Holt Geometry 6-1 Properties and Attributes of Polygons Example 2B: Classifying Polygons Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, concave

18. Holt Geometry 6-1 Properties and Attributes of Polygons Example 2C: Classifying Polygons Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. regular, convex

19. Holt Geometry 6-1 Properties and Attributes of Polygons Check It Out! Example 2a Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. regular, convex

20. Holt Geometry 6-1 Properties and Attributes of Polygons Check It Out! Example 2b Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, concave

21. Holt Geometry 6-1 Properties and Attributes of Polygons To find the sum of the interior angle measures of a convex polygon, draw all possible diagonals from one vertex of the polygon. This creates a set of triangles. The sum of the angle measures of all the triangles equals the sum of the angle measures of the polygon.

22. Holt Geometry 6-1 Properties and Attributes of Polygons By the Triangle Sum Theorem, the sum of the interior angle measures of a triangle is 180°. Remember!

23. Holt Geometry 6-1 Properties and Attributes of Polygons Note 42

24. Holt Geometry 6-1 Properties and Attributes of Polygons In each convex polygon, the number of triangles formed is two less than the number of sides n. So the sum of the angle measures of all these triangles is (n — 2)180°.

25. Holt Geometry 6-1 Properties and Attributes of Polygons Example 3A: Finding Interior Angle Measures and Sums in Polygons Find the sum of the interior angle measures of a convex heptagon.

26. Holt Geometry 6-1 Properties and Attributes of Polygons Example 3C: Finding Interior Angle Measures and Sums in Polygons Find the measure of each interior angle of pentagon ABCDE.

27. Holt Geometry 6-1 Properties and Attributes of Polygons Check It Out! Example 3a Find the sum of the interior angle measures of a convex 15-gon.