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Polygons

Polygons. The word ‘ poly gon ’ is a Greek word. Poly means many and gon means angles. Examples of Polygons. These are not Polygons. Terminology. Side: One of the line segments that make up a polygon. Vertex: Point where two sides meet. Vertex. Side.

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Polygons

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

  2. Examples of Polygons Polygons

  3. These are not Polygons Polygons

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

  5. Vertex Side Polygons

  6. 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

  7. Exterior angle Interior angle Polygons

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

  9. 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

  10. 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

  11. Examples of Regular Polygons Polygons

  12. 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

  13. IN TERIOR ANGLES OF A POLYGON Polygons

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

  15. 180o 180o 180o 180o 2 1 diagonal 3 x 180o = 540o 180o 5 180o 180o 180o 180o 180o 4 sides Quadrilateral 5 sides Pentagon 2 x 180o = 360o 3 2 diagonals 180o 180o 180o 180o 6 sides Hexagon Heptagon/Septagon 7 sides 4 x 180o = 720o 4 5 x 180o = 900o 3 diagonals 4 diagonals Polygons

  16. Polygons

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  23. 1 Calculate the Sum of Interior Angles and each interior angle of each of these regular polygons. 7 sides Septagon/Heptagon Sum of Int. Angles 900o Interior Angle 128.6o 2 3 4 9 sides 10 sides 11 sides Nonagon Decagon Hendecagon Sum 1260o I.A. 140o Sum 1440o I.A. 144o Sum 1620o I.A. 147.3o Polygons

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

  25. EXTERIOR ANGLES OF A POLYGON Polygons

  26. B A C F 1 2 E D Y 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 =1800 Polygons

  27. 1200 600 1200 600 600 1200 Polygons

  28. 1200 1200 1200 Polygons

  29. 1200 1200 1200 Polygons

  30. 3600 Polygons

  31. 600 600 600 600 600 600 Polygons

  32. 600 600 600 600 600 600 Polygons

  33. 3 4 2 5 1 6 600 600 600 600 600 600 Polygons

  34. 3 4 600 600 2 600 600 5 600 600 1 6 Polygons

  35. 3 4 2 3600 5 1 6 Polygons

  36. 900 900 900 900 Polygons

  37. 900 900 900 900 Polygons

  38. 900 900 900 900 Polygons

  39. 2 3 3600 1 4 Polygons

  40. 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

  41. In a regular polygon with ‘n’ sides Sum of interior angles = (n -2) x 1800 i.e. 2(n – 2) x right angles Exterior Angle + Interior Angle =1800 Each exterior angle = 3600/n No. of sides = 3600/exterior angle Polygons

  42. Let us explore few more problems • Find the measure of each interior angle of a polygon with 9 sides. • Ans : 1400 • Find the measure of each exterior angle of a regular decagon. • Ans : 360 • How many sides are there in a regular polygon if each interior angle measures 1650? • Ans : 24 sides • Is it possible to have a regular polygon with an exterior angle equal to 400 ? • Ans : Yes Polygons

  43. Thank You Polygons DG

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