Polygon: Definition, Terminologies and Kinds
- 1. Polygons The word ‘polygon’ is a Greek word. Poly means many and gon means angles.
- 2. Polygons Polygons • The word polygon means “many angles” • A two dimensional object • A closed figure
- 3. 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
- 5. These are not Polygons Polygons
- 6. Terminology Side: One of the line segments that make up a polygon. Vertex: Point where two sides meet. Polygons
- 8. • 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
- 10. Let us recapitulate Interior angle Diagonal Vertex Side Exterior angle Polygons
- 11. 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
- 12. • 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
- 13. Examples of Regular Polygons Polygons
- 14. 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
- 15. INTERIOR ANGLES OF A POLYGON Polygons
- 16. Let us find the connection between the number of sides, number of diagonals and the number of triangles of a polygon. Polygons
- 17. Quadrilateral Pentagon 180 o 180 o 180o 180o 180o 2 x 180o = 360o 3 4 sides 5 sides 3 x 180 o = 540 o Hexagon 6 sides 180o 180o 180o 180o 4 x 180o = 720o 4 Heptagon/Septagon 7 sides 180o 180o 180o 180o 180o 5 x 180o = 900o 5 2 1 diagonal 2 diagonals 3 diagonals 4 diagonals Polygons
- 18. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 0 1 180 0 180 0 /3 = 60 0 Polygons
- 19. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 0 1 180 0 180 0 /3 = 60 0 Quadrilateral 4 1 2 2 x180 0 = 360 0 360 0 /4 = 90 0 Polygons
- 20. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 0 1 180 0 180 0 /3 = 60 0 Quadrilateral 4 1 2 2 x180 0 = 360 0 360 0 /4 = 90 0 Pentagon 5 2 3 3 x180 0 = 540 0 540 0 /5 = 108 0 Polygons
- 21. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 0 1 180 0 180 0 /3 = 60 0 Quadrilateral 4 1 2 2 x180 0 = 360 0 360 0 /4 = 90 0 Pentagon 5 2 3 3 x180 0 = 540 0 540 0 /5 = 108 0 Hexagon 6 3 4 4 x180 0 = 720 0 720 0 /6 = 120 0 Polygons
- 22. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 0 1 180 0 180 0 /3 = 60 0 Quadrilateral 4 1 2 2 x180 0 = 360 0 360 0 /4 = 90 0 Pentagon 5 2 3 3 x180 0 = 540 0 540 0 /5 = 108 0 Hexagon 6 3 4 4 x180 0 = 720 0 720 0 /6 = 120 0 Heptagon 7 4 5 5 x180 0 = 900 0 900 0 /7 = 128.3 0 Polygons
- 23. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 0 1 180 0 180 0 /3 = 60 0 Quadrilateral 4 1 2 2 x180 0 = 360 0 360 0 /4 = 90 0 Pentagon 5 2 3 3 x180 0 = 540 0 540 0 /5 = 108 0 Hexagon 6 3 4 4 x180 0 = 720 0 720 0 /6 = 120 0 Heptagon 7 4 5 5 x180 0 = 900 0 900 0 /7 = 128.6 0 “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
- 24. Regular Polygon No. of sides No. of diagonals No. of Sum of the interior angles Each interior angle Triangle 3 0 1 180 0 180 0 /3 = 60 0 Quadrilateral 4 1 2 2 x180 0 = 360 0 360 0 /4 = 90 0 Pentagon 5 2 3 3 x180 0 = 540 0 540 0 /5 = 108 0 Hexagon 6 3 4 4 x180 0 = 720 0 720 0 /6 = 120 0 Heptagon 7 4 5 5 x180 0 = 900 0 900 0 /7 = 128.6 0 “n” sided polygon n n - 3 n - 2 (n - 2) x180 0 (n - 2) x180 0 / n Polygons
- 25. Septagon/Heptagon Decagon Hendecagon 7 sides 10 sides 11 sides 9 sides Nonagon Sum of Int. Angles 900 o Interior Angle 128.6o Sum 1260 o I.A. 140 o Sum 1440o I.A. 144 o Sum 1620o 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
- 26. 2 x 180o = 360o 360 – 245 = 115o 3 x 180o = 540o 540 – 395 = 145o y 117o 121o 100o 125o 140o z 133o 137o 138o 138o 125o 105o Find the unknown angles below. Diagrams not drawn accurately. 75o 100o 70o w x 115o 110o 75o 95o 4 x 180o = 720o 720 – 603 = 117o 5 x 180o = 900o 900 – 776 = 124o Polygons
- 27. EXTERIOR ANGLES OF A POLYGON Polygons
- 28. An exterior angle of a regular polygon is formed by extending one side of the polygo Angle CDY is an exterior angle to angle CDE Exterior Angle + Interior Angle of a regular polygon =180 0 D E Y B C A F 1 2 Polygons
- 32. 3600 Polygons
- 42. 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
- 43. In a regular polygon with ‘n’ sides Sum of interior angles = (n -2) x 180 0 i.e. 2(n – 2) x right angles Exterior Angle + Interior Angle =180 0 Each exterior angle = 360 0 /n No. of sides = 360 0 /exterior angle Polygons
- 44. Let us explore few more problems • Find the measure of each interior angle of a polygon with 9 sides. • Ans : 140 0 • Find the measure of each exterior angle of a regular decagon. • Ans : 36 0 • 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
- 45. Polygons DG
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