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1. POLYGONS

2. WARM UP!!!

3. not a polygon polygon

4. What is a polygon? • A polygon is a plane figure. • A polygon is a closed region. • A polygon is formed by three or more line segments as its sides. • Each side of a polygon intersects only one segment at each of its endpoints. • poli “many angled”

5. Polygon or Not a Polygon?

6. Polygon or Not a Polygon? Polygon

7. Polygon or Not a Polygon?

8. Polygon or Not a Polygon? Not Polygon because sides are not line segments.

9. Polygon or Not a Polygon?

10. Polygon or Not a Polygon? Not Polygon because sides are intersecting at more than the endpoints.

11. Polygon or Not a Polygon?

12. Polygon or Not a Polygon? Polygon

13. Polygon or Not a Polygon?

14. Polygon or Not a Polygon? Not Polygon because sides are not intersecting at the endpoints.

15. Polygon or Not a Polygon?

16. Polygon or Not a Polygon? Polygon

17. Polygon or Not a Polygon?

18. Polygon or Not a Polygon? Not Polygon because sides are intersecting more than one other side at its endpoint.

19. Naming Polygons • Polygons are named by writing their consecutive vertices in order, such as ABCD or CDAB for the polygon above. • We cannot name the polygon as DBAC. A B D C

20. Polygons can be named by their number of sides.

21. Connecting to Prior Knowledge • Think of words beginning with the prefixes tri-, quad-, pent-, and oct-. • Examples: triathlon, quadriplegic, pentameter, and octopus.

22. Regions in a Polygon

23. Parts of a Polygon • sides • consecutive sides • included angle • nonconsecutive sides • interior angles / vertex angles • consecutive angles • included side • nonconsecutive angles • exterior angles

24. Interior Angles of Polygons • In a triangle the sum of the interior angles =180o • In a quadrilateral the sum of the interior angles =360o USING WHAT YOU KNOW ABOUT TRIANGLES PROVE IT!!

25. Interior Angles of Polygons • Now how about a pentagon? • In a pentagon the sum of the interior angles =540o

26. Interior Angles of Polygons • In any polygon, the sum of the interior angles is: 180 (sides – 2) • NOTE: sides-2 is equal to the number of triangles you can form in the interior of the polygon! • What is the sum of interior angles in a: • Hexagon – 720o • Octagon - 1080o • Decagon - 1440o

27. ALL POLYGONS???

28. ALL POLYGONS!

29. How can these polygons be divided into two groups?

30. Concave Polygons Convex Polygons

31. Polygon Convexity A polygonal region is convex if any segment joining any two points of the polygon is part of the interior region. If a polygon is not convex, then its is concave.

32. Convex or Concave? Convex

33. Convex or Concave? Concave because a segment connecting points on the polygon that will lie in the exterior can be drawn.

34. Convex or Concave? Convex

35. Convex or Concave? Concave A segment connecting points on the polygon will lie in the exterior.

36. Convex or Concave? Concave A segment connecting points on the polygon will lie in the exterior.

37. Convex or Concave? Convex

38. Convex or Concave? Concave A segment connecting points on the polygon will lie in the exterior.

39. Concepts • EQUIANGULAR POLYGON • EQUILATERAL POLYGON • REGULAR POLYGON

40. EQUILATERAL but not EQUIANGULAR EQUILATERAL and EQUIANGULAR ┌ ┌ ┌ ┌ EQUILATERAL and EQUIANGULAR EQUIANGULAR but not EQUILATERAL ┌ ┌ ┌ ┌

41. Regular vs. Irregular polygons Which of these is a regular pentagon?

42. Regular vs. Irregular polygons Regular polygons are equilateral and equiangular Examples??? Square, regular pentagon, equilateral triangle Counterexamples??? Kite, rhombus, trapezoid, parallelogram, isosceles triangle

43. Parts of a Polygon • Diagonals • A diagonal of a polygon is any segment that joins two nonconsecutive vertices. Figure shows five-sided polygon QRSTU. Segments QS , SU , UR , RT and QT are the diagonals in this polygon.

44. Practice Exercise Set 6.1 on pages 280-282 #1-6, 9-12, 18, 19 • B. C. D.

45. not a polygon polygon