w.6 Gr.6 L(3.1)Polygons.pptxw.6 Gr.6 L(3.1)Polygons.pptx

w.6 Gr.6 L(3.1)Polygons.pptx

1. Polygons The word ‘ poly gon ’ is a Greek word. Poly means many and gon means angles. Areej Ahmed

2. Can you guess our lesson’s title ? According to the given video

3. Polygons Polygons The word polygon means “many angles” A two dimensional object A closed figure

4. Warm Up

5. Polygons and their angles The word polygon means “many angles” A two dimensional object A closed figure

6. More about Polygons Made up of three or more straight line segments. There are exactly two sides that meet at a vertex. The sides do not cross each other. Polygons

7. More about Polygons Made up of three or more straight line segments There are exactly two sides that meet at a vertex The sides do not cross each other Polygons

8. Keywords Side : One of the line segments that make up a polygon. Vertex : Point where two sides meet. Polygons

9. Examples of Polygons Polygons

10. These are not Polygons Polygons

11. Terminology Side: One of the line segments that make up a polygon. Vertex: Point where two sides meet. Polygons

12. Vertex Side Polygons

13. Interior angle: An angle formed by two adjacent sides inside the polygon. Exterior angle: An angle formed by two adjacent sides outside the polygon. Polygons

14. Interior angle Exterior angle Polygons

15. Let us recapitulate Interior angle Diagonal Vertex Side Exterior angle Polygons

16. Types of Polygons Equiangular Polygon: a polygon in which all of the angles are equal Equilateral Polygon: a polygon in which all of the sides are the same length Polygons

17. Regular Polygon: a polygon where all the angles are equal and all of the sides are the same length. They are both equilateral and equiangular Polygons

18. Examples of Regular Polygons Polygons

19. A convex polygon: A polygon whose each of the interior angle measures less than 180°. If one or more than one angle in a polygon measures more than 180° then it is known as concave polygon. ( Think: concave has a "cave" in it ) Polygons

20. IN TERIOR ANGLES OF A POLYGON Polygons

21. Let us find the connection between the number of sides, number of diagonals and the number of triangles of a polygon. Polygons

22. Quadrilateral Pentagon 180 o 180 o 180 o 180 o 180 o 2 x 180 o = 360 o 3 4 sides 5 sides 3 x 180 o = 540 o Hexagon 6 sides 180 o 180 o 180 o 180 o 4 x 180 o = 720 o 4 Heptagon/Septagon 7 sides 180 o 180 o 180 o 180 o 180 o 5 x 180 o = 900 o 5 2 1 diagonal 2 diagonals 3 diagonals 4 diagonals Polygons

23. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 1 180 180 / 3 = 60 Polygons

24. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 1 180 180 / 3 = 60 Quadrilateral 4 1 2 2 x180 = 360 360 / 4 = 90 Polygons

25. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 1 180 180 / 3 = 60 Quadrilateral 4 1 2 2 x180 = 360 360 / 4 = 90 Pentagon 5 2 3 3 x180 = 540 540 / 5 = 108 Polygons

26. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 1 180 180 / 3 = 60 Quadrilateral 4 1 2 2 x180 = 360 360 / 4 = 90 Pentagon 5 2 3 3 x180 = 540 540 / 5 = 108 Hexagon 6 3 4 4 x180 = 720 720 / 6 = 120 Polygons

27. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 1 180 180 / 3 = 60 Quadrilateral 4 1 2 2 x180 = 360 360 / 4 = 90 Pentagon 5 2 3 3 x180 = 540 540 / 5 = 108 Hexagon 6 3 4 4 x180 = 720 720 / 6 = 120 Heptagon 7 4 5 5 x180 = 900 900 / 7 = 128.3 Polygons

28. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 1 180 180 / 3 = 60 Quadrilateral 4 1 2 2 x180 = 360 360 / 4 = 90 Pentagon 5 2 3 3 x180 = 540 540 / 5 = 108 Hexagon 6 3 4 4 x180 = 720 720 / 6 = 120 Heptagon 7 4 5 5 x180 = 900 900 / 7 = 128.3 “n” sided polygon n Association with no. of sides Association with no. of sides Association with no. of triangles Association with sum of interior angles Polygons

29. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 1 180 180 / 3 = 60 Quadrilateral 4 1 2 2 x180 = 360 360 / 4 = 90 Pentagon 5 2 3 3 x180 = 540 540 / 5 = 108 Hexagon 6 3 4 4 x180 = 720 720 / 6 = 120 Heptagon 7 4 5 5 x180 = 900 900 / 7 = 128.3 “n” sided polygon n n - 3 n - 2 (n - 2) x180 (n - 2) x180 / n Polygons

30. Septagon/Heptagon Decagon Hendecagon 7 sides 10 sides 11 sides 9 sides Nonagon Sum of Int. Angles 900 o Interior Angle 128.6 o Sum 1260 o I.A. 140 o Sum 1440 o I.A. 144 o Sum 1620 o I.A. 147.3 o Calculate the Sum of Interior Angles and each interior angle of each of these regular polygons. 1 2 4 3 Polygons

31. 2 x 180 o = 360 o 360 – 245 = 115 o 3 x 180 o = 540 o 540 – 395 = 145 o y 117 o 121 o 100 o 125 o 140 o z 133 o 137 o 138 o 138 o 125 o 105 o Find the unknown angles below. Diagrams not drawn accurately. 75 o 100 o 70 o w x 115 o 110 o 75 o 95 o 4 x 180 o = 720 o 720 – 603 = 117 o 5 x 180 o = 900 o 900 – 776 = 124 o Polygons

32. EXTERIOR ANGLES OF A POLYGON Polygons

33. An exterior angle of a regular polygon is formed by extending one side of the polygon. Angle CDY is an exterior angle to angle CDE Exterior Angle + Interior Angle of a regular polygon =180 D E Y B C A F 1 2 Polygons

34. 120 120 120 60 60 60 Polygons

35. 120 120 120 Polygons

36. 120 120 120 Polygons

37. 360 Polygons

38. 60 60 60 60 60 60 Polygons

39. 60 60 60 60 60 60 Polygons

40. 1 2 3 4 5 6 60 60 60 60 60 60 Polygons

41. 1 2 3 4 5 6 60 60 60 60 60 60 Polygons

42. 1 2 3 4 5 6 360 Polygons

43. 90 90 90 90 Polygons

44. 90 90 90 90 Polygons

45. 90 90 90 90 Polygons

46. 1 2 3 4 360 Polygons

47. No matter what type of polygon we have, the sum of the exterior angles is ALWAYS equal to 360º.   Sum of exterior angles = 360º Polygons

48. In a regular polygon with ‘n’ sides Sum of interior angles = (n -2) x 180 i.e. 2(n – 2) x right angles Exterior Angle + Interior Angle =180 Each exterior angle = 360 /n No. of sides = 360 /exterior angle                Polygons

49. Let us explore few more problems Find the measure of each interior angle of a polygon with 9 sides. Ans : 140 Find the measure of each exterior angle of a regular decagon. Ans : 36 How many sides are there in a regular polygon if each interior angle measures 165 ? Ans : 24 sides Is it possible to have a regular polygon with an exterior angle equal to 40 ? Ans : Yes Polygons

50. Polygons DG Thank You

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