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Quadrilateral Angle Sum Theorems Demo

Quadrilateral Angle Sum Theorems Demo
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2015-10-22 22:41
PolygonAngleGeometric ConstructionSlider Animation
In collections Polygons & Angles Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles Polygons & Angles Polygons & Angles Polygons & Angles Geometry: Polygons & Angles Geometry: Polygons & Angles
This applet informally demonstrates to students that the sum of the interior angles of any quadrilateral is 360 degrees, and explores properties of exterior angles. It involves core math concepts like polygon angle sum theorem and exterior angle properties. Constructed using GeoGebra commands such as Ray, Point, Circle, Intersect, Segment, Angle, CircleSector, Vector, Translate, Dilate, Rotate, Mirror, Line, Polygon. Suitable for middle school and above students to visually grasp quadrilateral angle properties and enhance spatial reasoning.

GeoGebra Commands & Parameters

  1. Ray(P, A) → h_1
  2. Point(h_1) → R
  3. Ray(A, R) → j_1
  4. Ray(A, B) → a
  5. Circle(A, 1.5) → g
  6. Intersect(g, j_1) → I_1,
  7. Intersect(g, a, 1) → H
  8. Segment(P, A) → l_1
  9. Intersect(g, l_1, 1) → H_1
  10. Segment(P, C) → k_1
  11. Circle(C, 1.5) → k
  12. Intersect(k, k_1) → Z,
  13. Ray(B, C) → b
  14. Intersect(k, b) → M, N
  15. Ray(C, A) → c
  16. Point(a) → D_1
  17. Point(b) → E_1
  18. Point(c) → F_1
  19. Ray(A, F_1) → d
  20. Ray(B, D_1) → e
  21. Ray(C, E_1) → f
  22. Point(e) → D
  23. Point(f) → E
  24. Angle(C, B, A) → β
  25. Angle(A, C, B) → γ
  26. Angle(D, B, C) → ε
  27. Angle(E, C, A) → ζ
  28. Circle(B, 1.5) → h
  29. Intersect(g, c, 1) → G
  30. Intersect(g, c, 2) → I
  31. Intersect(h, b, 1) → J
  32. Intersect(h, a, 1) → K
  33. Intersect(h, a, 2) → L
  34. Intersect(k, c) → O,
  35. CircleSector(C, Z, M) → r
  36. CircleSector(B, J, K) → q
  37. CircleSector(B, L, J) → t
  38. Vector(B, C) → u
  39. CircleSector(A, I_1, H) → c_1
  40. Vector(A, C) → v
  41. Translate(q, u) → q'
  42. Segment(B, C) → l
  43. Dilate(C, If[0 < j ≤ 1, j, 0], B) → C'
  44. Vector(B, C') → w
  45. Translate(q, w) → q'_1
  46. Rotate(q'_1, If[0 < j, (((-j) * 180))°, 180*°], C') → d_1
  47. Mirror(q', C) → q''
  48. Dilate(A, If[1 < j ≤ 2, 2 - j, 0], C) → C'_1
  49. Vector(A, C'_1) → m
  50. CircleSector(A, H, H_1) → p
  51. Translate(p, m) → p'
  52. Dilate(C, If[0 < n ≤ 1, n, 0], B) → C'_2
  53. Dilate(A, If[1 < n ≤ 2, 2 - n, 0], C) → A'
  54. Vector(B, C'_2) → u_1
  55. Vector(A, A') → v_1
  56. If(0 < n ≤ 1, Translate[t, u_1], Translate[t, u]) → e_1
  57. If(1 < n ≤ 2, Translate[c_1, v_1], Translate[c_1, v]) → f_1
  58. Ray(C, P) → g_1
  59. Point(g_1) → Q
  60. Ray(P, Q) → i_1
  61. Point(i_1) → S
  62. Point(j_1) → T
  63. Circle(P, 1.5) → p_1
  64. Intersect(p_1, l_1) → U,
  65. Intersect(p_1, i_1) → V,
  66. Intersect(p_1, k_1) → W,
  67. CircleSector(P, U, W) → q_1
  68. Intersect(k, b, 2) → A_1
  69. Intersect(k, r, 1) → B_1
  70. Line(P, b) → b_1
  71. Intersect(p_1, b_1) → C_1, G_1
  72. Angle(B, A, P) → α
  73. Vector(P, C) → i
  74. Rotate(p', If[1 < j ≤ 2, 0*°, 0*°], C'_1) → p''
  75. Dilate(P, If[2 < j ≤ 3, 3 - j, 0], C) → P'
  76. Vector(P, P') → w_1
  77. Translate(q_1, w_1) → r_1
  78. Rotate(r_1, If[2 < j ≤ 3, (((j - 2) * 180))°, 180*°], P') → s_1
  79. CircleSector(C, N, Z) → s
  80. CircleSector(P, V, U) → t_1
  81. Dilate(P, If[2 < n ≤ 3, 3 - n, 0], C) → P'_1
  82. Vector(P, P'_1) → m_1
  83. If(2 < n ≤ 3, Translate[t_1, m_1], Translate[t_1, w_1]) → e_2
  84. Angle(H, A, I_1) → δ
  85. Angle(V, P, U) → η
  86. Angle(U, P, W) → θ
  87. Polygon(A, B, C, P) → poly1, a_2, b_2, c_2, p_2