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Kite and Polygon Animation Demo

Kite and Polygon Animation Demo
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2016-06-16 09:34
PolygonVectorCoordinate GeometryGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
This example demonstrates the construction and properties of kites and polygons through animation. It involves core math concepts like coordinate geometry, vectors, transformations, and geometric construction. Key GeoGebra commands used include Segment, Midpoint, OrthogonalLine, Circle, Intersect, Rotate, Polygon, and Vector. Suitable for high school mathematics education to understand geometric transformations and polygonal properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Midpoint(a) → C
  3. OrthogonalLine(C, a) → b
  4. Point(b) → E
  5. Point(b) → G_1
  6. Ray(E, G_1) → h_2
  7. Point(h_2) → D
  8. Segment(C, D) → i
  9. Circle(D, (0.3 * i)) → q
  10. Intersect(q, h_2, 1) → H_1
  11. Segment(A, D) → c
  12. Intersect(q, c, 1) → K
  13. Segment(D, B) → d
  14. Segment(B, E) → e
  15. Segment(E, A) → f
  16. Segment(A, C) → g
  17. Circle(A, (0.3 * g)) → h
  18. Circle(B, (0.3 * g)) → k
  19. Segment(C, E) → j
  20. Circle(E, (0.3 * j)) → p
  21. Circle(C, (0.3 * g)) → r
  22. Intersect(h, f, 1) → F
  23. Intersect(h, c, 1) → G
  24. Intersect(k, e, 1) → H
  25. Intersect(k, d, 1) → I
  26. Intersect(q, d, 1) → J
  27. Intersect(p, e, 1) → L
  28. Intersect(b, j) → M
  29. Intersect(b, j) → N
  30. Intersect(b, j) → O
  31. Intersect(b, j) → P
  32. Intersect(b, j) → Q
  33. Intersect(p, b, 2) → R
  34. Intersect(b, i) → S
  35. Intersect(q, b, 1) → T
  36. Intersect(p, f, 1) → U
  37. CircleSector(B, I, H) → s
  38. Angle(A, D, B) → α
  39. Angle(U, E, L) → β
  40. CircleSector(B, H, I) → t
  41. Dilate(D, If[0 < l ≤ 1, 1 - l, 0], A) → D'
  42. Segment(D, D') → m
  43. Rotate(D, If[1 < l ≤ 2, ((l - 1) * α), α], D) → D'_1
  44. Rotate(D', If[1 < l ≤ 2, ((l - 1) * α), α], D) → D''
  45. Segment(D'_1, D'') → m'
  46. Dilate(A, If[2 < l ≤ 3, 3 - l, 0], E) → A'
  47. Segment(A, A') → n
  48. Rotate(A, If[3 < l ≤ 4, ((-(l - 3)) * ((2 * π) - β)), (-((2 * π) - β))], E) → A'_1
  49. Rotate(A', If[3 < l ≤ 4, ((-(l - 3)) * ((2 * π) - β)), (-((2 * π) - β))], E) → A''
  50. Segment(A'_1, A'') → n'
  51. Polygon(E, B, D, A) → poly1, e_1, b_1, d_1, a_1
  52. CircleSector(E, L, R) → f_1
  53. Dilate(D, If[4 < l ≤ 5, 5 - l, 0], E) → D'_2
  54. Segment(D, D'_2) → g_1
  55. Dilate(B, If[5 < l ≤ 6, 6 - l, 0], A) → B'
  56. Vector(B, B') → u
  57. Translate(s, u) → s'
  58. Line(A, e) → h_1
  59. Intersect(h, h_1, 2) → V
  60. Intersect(h, g, 1) → W
  61. Angle(V, A, G) → γ
  62. Rotate(s', If[6 < l ≤ 7, ((l - 6) * γ), γ], A) → s''
  63. CircleSector(D, K, H_1) → c_1
  64. Rotate(f_1, If[8 < l ≤ 9, ((l - 8) * ((2 * π) - β) / 2), ((2 * π) - β) / 2], E) → p_1
  65. Dilate(A, If[9 < l ≤ 10, 10 - l, 0], C) → A'_2
  66. Segment(A, A'_2) → i_1
  67. Dilate(C, If[10 < l ≤ 11, 11 - l, 0], B) → D'_3
  68. Segment(C, D'_3) → j_1
  69. Segment(B, C) → l_1
  70. Intersect(k, l_1, 1) → Z
  71. CircleSector(B, I, Z) → q_1
  72. CircleSector(A, F, W) → r_1
  73. Rotate(C, If[11.5 < l ≤ 12.5, ((l - 11.5) * π), 3.141592653589793], C) → C'
  74. Rotate(D'_3, If[11.5 < l ≤ 12.5, ((l - 11.5) * π), 3.141592653589793], C) → A_1
  75. Segment(C', A_1) → m_1
  76. Dilate(A, If[12.5 < l ≤ 13.5, 13.5 - l, 0], B) → A'_3
  77. Vector(A, A'_3) → v
  78. Translate(r_1, v) → s_1
  79. Line(B, n) → n_1
  80. Point(n_1) → B_1
  81. Ray(B, B_1) → t_1
  82. Point(t_1) → C_1
  83. Angle(H, B, C_1) → δ
  84. Angle(Z, B, H) → ε
  85. Rotate(s_1, If[13.5 < l ≤ 14.5, ((-(l - 13.5)) * (ε + δ)), (-(ε + δ))], B) → c_2
  86. Dilate(B, If[14.5 < l ≤ 15.5, 15.5 - l, 0], A) → B'_1
  87. Vector(B, B'_1) → w
  88. Translate(q_1, w) → d_2
  89. Translate(I, w) → I'
  90. Angle(G, A, I') → ζ
  91. Angle(D, B, C) → η
  92. Rotate(d_2, If[15.5 < l ≤ 16.5, ((-(l - 15.5)) * (ζ + η)), (-(ζ + η))], A) → e_2
  93. Midpoint(A, B) → D_1
  94. Segment(D, E) → a_2
  95. Segment(A, B) → b_2
  96. Intersect(r, a_2, 2) → E_1
  97. Intersect(r, b_2, 2) → F_1
  98. CircleSector(C, E_1, F_1) → f_2
  99. Rotate(f_2, If[16.5 < l ≤ 17.5, ((-(l - 16.5)) * π / 2), -1.5707963267948966], D_1) → g_2
  100. Rotate(c_1, If[7 < l ≤ 8, ((l - 7) * α / 2), α / 2], D) → k_1