1. Polygons and Quadrilaterals I can classify polygons and find their angle measures.

2. The Polygon Angle-Sum Theorems Sketch a convex, triangle, quadrilateral, pentagon, and hexagon. For each figure, draw all the diagonals you can from one vertex. What conjecture can you make about the relationship between the number of sides of a polygon and the number triangles formed by the diagonals from one vertex?

3. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon

4. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle3 Quadrilateral Pentagon Hexagon Heptagon Octagon

5. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle3 Quadrilateral4 Pentagon Hexagon Heptagon Octagon

6. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle3 Quadrilateral4 Pentagon5 Hexagon Heptagon Octagon

7. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle3 Quadrilateral4 Pentagon5 Hexagon6 Heptagon Octagon

8. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle3 Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon

9. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle3 Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon8

10. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31 Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon8

11. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31 Quadrilateral42 Pentagon5 Hexagon6 Heptagon7 Octagon8

12. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31 Quadrilateral42 Pentagon53 Hexagon6 Heptagon7 Octagon8

13. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31 Quadrilateral42 Pentagon53 Hexagon64 Heptagon7 Octagon8

14. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31 Quadrilateral42 Pentagon53 Hexagon64 Heptagon75 Octagon8

15. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31 Quadrilateral42 Pentagon53 Hexagon64 Heptagon75 Octagon86

16. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31180 Quadrilateral42 Pentagon53 Hexagon64 Heptagon75 Octagon86

17. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31180 Quadrilateral42360 Pentagon53 Hexagon64 Heptagon75 Octagon86

18. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31180 Quadrilateral42360 Pentagon53540 Hexagon64 Heptagon75 Octagon86

19. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31180 Quadrilateral42360 Pentagon53540 Hexagon64720 Heptagon75 Octagon86

20. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31180 Quadrilateral42360 Pentagon53540 Hexagon64720 Heptagon75900 Octagon86

21. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31180 Quadrilateral42360 Pentagon53540 Hexagon64720 Heptagon75900 Octagon861080

22. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31180 Quadrilateral42360 Pentagon53540 Hexagon64720 Heptagon75900 Octagon861080 N-gonn

23. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31180 Quadrilateral42360 Pentagon53540 Hexagon64720 Heptagon75900 Octagon861080 N-gonnn-2

24. Polygon Angle-Sum PolygonNumber of SidesNumber of Triangles Formed Angle-Sum Triangle31180 Quadrilateral42360 Pentagon53540 Hexagon64720 Heptagon75900 Octagon861080 N-gonnn-2(n-2)180

25. Theorem: Polygon Angle-Sum Thm. The sum of the measures of the interior angles of an n-gon is (n - 2)180. Ex. What is the sum of the interior angle measures of a 17-gon?

26. Theorem: Polygon Angle-Sum Thm. The sum of the measures of the interior angles of an n-gon is (n - 2)180. Ex. What is the sum of the interior angle measures of a 17-gon? Sum = (n – 2)180

27. Theorem: Polygon Angle-Sum Thm. The sum of the measures of the interior angles of an n-gon is (n - 2)180. Ex. What is the sum of the interior angle measures of a 17-gon? Sum = (n – 2)180 Sum = (17 – 2)180

28. Theorem: Polygon Angle-Sum Thm. The sum of the measures of the interior angles of an n-gon is (n - 2)180. Ex. What is the sum of the interior angle measures of a 17-gon? Sum = (n – 2)180 Sum = (17 – 2)180 Sum = 15 180

29. Theorem: Polygon Angle-Sum Thm. The sum of the measures of the interior angles of an n-gon is (n - 2)180. Ex. What is the sum of the interior angle measures of a 17-gon? Sum = (n – 2)180 Sum = (17 – 2)180 Sum = 15 180 Sum = 2700

30. Theorem: Polygon Angle-Sum Thm. The sum of the measures of the interior angles of an n-gon is (n - 2)180. Reasoning: The sum of the interior angle measures of a polygon is 1980. How can you find the number of sides in the polygon?

31. Corollary to the Polygon Angle-Sum Thm.

35. Theorem: Polygon Exterior Angle-Sum The sum of the measures of the exterior angles of a polygon, one from each vertex, is 360. Ex. What is the measure of an exterior angle of a regular octagon?

36. Theorem: Polygon Exterior Angle-Sum