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Interior Angles of Polygons by pchou

Interior Angles of Polygons by pchou
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2015-11-23 06:12
PolygonAngleGeometric Construction
This example demonstrates the properties and calculation methods of interior angles in polygons. Key math concepts include the sum of interior angles formula, angle measurement, and geometric construction. GeoGebra commands and objects used in the construction summary are Intersect, Circle, Sequence, Row, and Angle. Suitable for middle school and above students to learn and understand the relevant knowledge of polygon interior angles, can be used for classroom teaching or self-exploration.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Sequence(Rotate[B, ((-2 * 3.141592653589793 / Sides) * j), A], j, 1, Sides) → list1
  4. Sequence(Segment[Element[list1, Mod[j, Sides] + 1], Element[list1, Mod[j + 1, Sides] + 1]], j, 1, Sides) → list2
  5. Row(A2) → B2
  6. Sequence(Angle[Element[list1, Mod[j, Sides] + 1], Element[list1, Mod[j + 1, Sides] + 1], Element[list1, Mod[j + 2, Sides] + 1]], j, 1, Sides) → list3
  7. Row(A1) → B1
  8. Angle(Element[list1, Mod[1, Sides] + 1], Element[list1, Mod[2, Sides] + 1], Element[list1, Mod[3, Sides] + 1]) → α
  9. Row(A3) → B3
  10. Row(A4) → B4
  11. Row(A5) → B5
  12. Row(A6) → B6
  13. Row(A7) → B7
  14. Row(A8) → B8
  15. Row(A9) → B9
  16. Row(A10) → B10
  17. Row(A11) → B11
  18. Row(A12) → B12
  19. Row(A13) → B13
  20. Row(A14) → B14
  21. Row(A15) → B15
  22. Row(A16) → B16
  23. Row(A17) → B17
  24. Row(A18) → B18
  25. Row(A19) → B19
  26. Row(A20) → B20
  27. Row(A21) → B21
  28. Row(A22) → B22
  29. Row(A23) → B23
  30. Row(A24) → B24
  31. Row(A25) → B25
  32. Row(A26) → B26
  33. Row(A27) → B27
  34. Row(A28) → B28
  35. Row(A29) → B29
  36. Row(A30) → B30
  37. Row(A31) → B31
  38. Row(A32) → B32
  39. Row(A33) → B33
  40. Row(A34) → B34
  41. Row(A35) → B35
  42. Row(A36) → B36
  43. Angle(Element[list1, Mod[B1, Sides] + 1], Element[list1, Mod[B1 + 1, Sides] + 1], Element[list1, Mod[B1 + 2, Sides] + 1]) → C1
  44. Angle(Element[list1, Mod[B2, Sides] + 1], Element[list1, Mod[B2 + 1, Sides] + 1], Element[list1, Mod[B2 + 2, Sides] + 1]) → C2
  45. Angle(Element[list1, Mod[B3, Sides] + 1], Element[list1, Mod[B3 + 1, Sides] + 1], Element[list1, Mod[B3 + 2, Sides] + 1]) → C3
  46. Angle(Element[list1, Mod[B4, Sides] + 1], Element[list1, Mod[B4 + 1, Sides] + 1], Element[list1, Mod[B4 + 2, Sides] + 1]) → C4
  47. Angle(Element[list1, Mod[B5, Sides] + 1], Element[list1, Mod[B5 + 1, Sides] + 1], Element[list1, Mod[B5 + 2, Sides] + 1]) → C5
  48. Angle(Element[list1, Mod[B6, Sides] + 1], Element[list1, Mod[B6 + 1, Sides] + 1], Element[list1, Mod[B6 + 2, Sides] + 1]) → C6
  49. Angle(Element[list1, Mod[B7, Sides] + 1], Element[list1, Mod[B7 + 1, Sides] + 1], Element[list1, Mod[B7 + 2, Sides] + 1]) → C7
  50. Angle(Element[list1, Mod[B8, Sides] + 1], Element[list1, Mod[B8 + 1, Sides] + 1], Element[list1, Mod[B8 + 2, Sides] + 1]) → C8
  51. Angle(Element[list1, Mod[B9, Sides] + 1], Element[list1, Mod[B9 + 1, Sides] + 1], Element[list1, Mod[B9 + 2, Sides] + 1]) → C9
  52. Angle(Element[list1, Mod[B10, Sides] + 1], Element[list1, Mod[B10 + 1, Sides] + 1], Element[list1, Mod[B10 + 2, Sides] + 1]) → C10
  53. Angle(Element[list1, Mod[B11, Sides] + 1], Element[list1, Mod[B11 + 1, Sides] + 1], Element[list1, Mod[B11 + 2, Sides] + 1]) → C11
  54. Angle(Element[list1, Mod[B12, Sides] + 1], Element[list1, Mod[B12 + 1, Sides] + 1], Element[list1, Mod[B12 + 2, Sides] + 1]) → C12
  55. Angle(Element[list1, Mod[B13, Sides] + 1], Element[list1, Mod[B13 + 1, Sides] + 1], Element[list1, Mod[B13 + 2, Sides] + 1]) → C13
  56. Angle(Element[list1, Mod[B14, Sides] + 1], Element[list1, Mod[B14 + 1, Sides] + 1], Element[list1, Mod[B14 + 2, Sides] + 1]) → C14
  57. Angle(Element[list1, Mod[B15, Sides] + 1], Element[list1, Mod[B15 + 1, Sides] + 1], Element[list1, Mod[B15 + 2, Sides] + 1]) → C15
  58. Angle(Element[list1, Mod[B16, Sides] + 1], Element[list1, Mod[B16 + 1, Sides] + 1], Element[list1, Mod[B16 + 2, Sides] + 1]) → C16
  59. Angle(Element[list1, Mod[B17, Sides] + 1], Element[list1, Mod[B17 + 1, Sides] + 1], Element[list1, Mod[B17 + 2, Sides] + 1]) → C17
  60. Angle(Element[list1, Mod[B18, Sides] + 1], Element[list1, Mod[B18 + 1, Sides] + 1], Element[list1, Mod[B18 + 2, Sides] + 1]) → C18
  61. Angle(Element[list1, Mod[B19, Sides] + 1], Element[list1, Mod[B19 + 1, Sides] + 1], Element[list1, Mod[B19 + 2, Sides] + 1]) → C19
  62. Angle(Element[list1, Mod[B20, Sides] + 1], Element[list1, Mod[B20 + 1, Sides] + 1], Element[list1, Mod[B20 + 2, Sides] + 1]) → C20
  63. Angle(Element[list1, Mod[B21, Sides] + 1], Element[list1, Mod[B21 + 1, Sides] + 1], Element[list1, Mod[B21 + 2, Sides] + 1]) → C21
  64. Angle(Element[list1, Mod[B22, Sides] + 1], Element[list1, Mod[B22 + 1, Sides] + 1], Element[list1, Mod[B22 + 2, Sides] + 1]) → C22
  65. Angle(Element[list1, Mod[B23, Sides] + 1], Element[list1, Mod[B23 + 1, Sides] + 1], Element[list1, Mod[B23 + 2, Sides] + 1]) → C23
  66. Angle(Element[list1, Mod[B24, Sides] + 1], Element[list1, Mod[B24 + 1, Sides] + 1], Element[list1, Mod[B24 + 2, Sides] + 1]) → C24
  67. Angle(Element[list1, Mod[B25, Sides] + 1], Element[list1, Mod[B25 + 1, Sides] + 1], Element[list1, Mod[B25 + 2, Sides] + 1]) → C25
  68. Angle(Element[list1, Mod[B26, Sides] + 1], Element[list1, Mod[B26 + 1, Sides] + 1], Element[list1, Mod[B26 + 2, Sides] + 1]) → C26
  69. Angle(Element[list1, Mod[B27, Sides] + 1], Element[list1, Mod[B27 + 1, Sides] + 1], Element[list1, Mod[B27 + 2, Sides] + 1]) → C27
  70. Angle(Element[list1, Mod[B28, Sides] + 1], Element[list1, Mod[B28 + 1, Sides] + 1], Element[list1, Mod[B28 + 2, Sides] + 1]) → C28
  71. Angle(Element[list1, Mod[B29, Sides] + 1], Element[list1, Mod[B29 + 1, Sides] + 1], Element[list1, Mod[B29 + 2, Sides] + 1]) → C29
  72. Angle(Element[list1, Mod[B30, Sides] + 1], Element[list1, Mod[B30 + 1, Sides] + 1], Element[list1, Mod[B30 + 2, Sides] + 1]) → C30
  73. Angle(Element[list1, Mod[B31, Sides] + 1], Element[list1, Mod[B31 + 1, Sides] + 1], Element[list1, Mod[B31 + 2, Sides] + 1]) → C31
  74. Angle(Element[list1, Mod[B32, Sides] + 1], Element[list1, Mod[B32 + 1, Sides] + 1], Element[list1, Mod[B32 + 2, Sides] + 1]) → C32
  75. Angle(Element[list1, Mod[B33, Sides] + 1], Element[list1, Mod[B33 + 1, Sides] + 1], Element[list1, Mod[B33 + 2, Sides] + 1]) → C33
  76. Angle(Element[list1, Mod[B34, Sides] + 1], Element[list1, Mod[B34 + 1, Sides] + 1], Element[list1, Mod[B34 + 2, Sides] + 1]) → C34
  77. Angle(Element[list1, Mod[B35, Sides] + 1], Element[list1, Mod[B35 + 1, Sides] + 1], Element[list1, Mod[B35 + 2, Sides] + 1]) → C35
  78. Angle(Element[list1, Mod[B36, Sides] + 1], Element[list1, Mod[B36 + 1, Sides] + 1], Element[list1, Mod[B36 + 2, Sides] + 1]) → C36
  79. Sequence(Polygon[Element[list1, Sides], Element[list1, j], Element[list1, j + 1]], j, 1, Sides - 2) → list4

AI Drawing Prompt Reference

Draw a polygon to demonstrate its interior angles. First, plot the x and y axes and let them intersect at the origin. Then, draw a circle centered at the origin. Divide the circle into several equal points and connect the adjacent points to form a polygon. Next, measure the angle between each pair of adjacent sides from each vertex and label them. Finally, highlight the angle at the first vertex formed by its adjacent sides and show the calculation process of the sum of interior angles.
The prompt above was compiled from the original drawing commands and is for reference only.