MathPlotAI Logo MathPlotAI

Dynamic Isosceles & Scalene Triangles Demo

Dynamic Isosceles & Scalene Triangles Demo
Loading the math board and drawing, please wait…
2018-02-06 09:25
TriangleCircleTrigonometryGeometric ConstructionSlider Animation
This example dynamically illustrates properties of isosceles and scalene triangles, focusing on area calculations and geometric transformations. Key concepts include isosceles triangles, scalene triangles, area, rational numbers, trigonometry, and rhombuses. Construction involves commands like Circle, Intersect, Dilate, Rotate, and Polygon. Suitable for high school mathematics education to explore geometric transformations and calculations.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Intersect(c, q) → O, P
  3. CircleArc(A, O, P) → d
  4. Point(d) → C
  5. Midpoint(C, A) → W
  6. Circle(W, 3) → t_1
  7. CircleArc(A, C, P) → e
  8. Point(e) → D
  9. Midpoint(C, D) → Q
  10. Midpoint(Q, A) → R
  11. Line(R, D) → n
  12. OrthogonalLine(Q, n) → s
  13. Intersect(n, s) → S
  14. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], S) → C'_2
  15. Segment(C, C'_2) → m_1
  16. Line(W, m_1) → b_1
  17. Point(b_1) → A_1
  18. Dilate(D, If[7 < j ≤ 8, 8 - j, 0], R) → D'
  19. Segment(D, D') → g_1
  20. Line(W, g_1) → n_1
  21. Intersect(t_1, n_1, 2) → Z
  22. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
  23. Segment(A, A') → a
  24. Angle(C, A, D) → α
  25. Rotate(A, If[1 < j ≤ 2, ((j - 1) * α), α], A) → A'_1
  26. Rotate(A', If[1 < j ≤ 2, ((j - 1) * α), α], A) → A''
  27. Segment(A'_1, A'') → a'
  28. Segment(A, C) → b
  29. Segment(C, D) → f
  30. Segment(D, A) → g
  31. Midpoint(f) → E
  32. Segment(A, E) → h
  33. Midpoint(h) → F
  34. Segment(A, F) → i
  35. Segment(F, E) → k
  36. Circle(A, (0.35 * i)) → p
  37. Circle(E, (0.15 * Distance[D, E])) → r
  38. Intersect(r, f, 2) → G
  39. Intersect(r, h, 1) → H
  40. Intersect(r, f, 1) → I
  41. Intersect(p, b, 1) → J
  42. Intersect(p, h, 1) → K
  43. Intersect(p, g, 1) → L
  44. Circle(A, B) → c_1
  45. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], D) → C'
  46. Segment(C, C') → l
  47. Polygon(C, D, A) → poly1, a_1, c_2, d_1
  48. Circle(C, (0.2 * Distance[D, E])) → e_1
  49. Intersect(e_1, b) → M,
  50. Intersect(e_1, f) → N,
  51. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], F) → A'_2
  52. Dilate(F, If[5 < j ≤ 6, 6 - j, 0], E) → F'
  53. Dilate(E, If[6 < j ≤ 7, 7 - j, 0], D) → E'
  54. Rotate(E, If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E'_1
  55. Rotate(E', If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E''
  56. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], D) → C'_1
  57. Vector(C, C'_1) → u
  58. Angle(E, C, A) → β
  59. CircleArc(A, C, A'') → s_1
  60. Line(A, Q) → m
  61. Angle(S, C, A) → γ
  62. Intersect(n, a) → T
  63. Angle(T, D, C) → δ
  64. Dilate(A, If[4 < j ≤ 5, 5 - j, 0], R) → A'_3
  65. Segment(A, A'_3) → t
  66. Dilate(R, If[5 < j ≤ 6, 6 - j, 0], Q) → R'
  67. Segment(R, R') → f_1
  68. Rotate(A, If[6 < j ≤ 7, ((j - 6) * π), π], R) → A'_4
  69. Rotate(A'_3, If[6 < j ≤ 7, ((j - 6) * π), π], R) → U
  70. Segment(A'_4, U) → t'
  71. Segment(D, S) → h_1
  72. Circle(D, (0.3 * h_1)) → k_1
  73. Circle(C, (0.3 * h_1)) → p_1
  74. Ray(C, S) → i_1
  75. Ray(C, A) → j_1
  76. Intersect(p_1, j_1) → V,
  77. Dilate(Q, If[8 < j ≤ 9, 9 - j, 0], S) → Q'
  78. Segment(Q, Q') → l_1
  79. Angle(D, S, Q) → ε
  80. Rotate(V, If[11 < j ≤ 12, ((-(j - 11)) * γ), (-γ)], C) → V'
  81. CircleSector(C, V', V) → q_1
  82. Dilate(C, If[12 < j ≤ 13, 13 - j, 0], W) → C'_3
  83. Vector(C, C'_3) → v
  84. Angle(A_1, W, Z) → ζ
  85. Translate(q_1, v) → r_1
  86. Rotate(r_1, If[13 < j ≤ 14, ((j - 13) * ζ), ζ], W) → d_2
  87. Dilate(W, If[14 < j ≤ 15, 15 - j, 0], D) → W'
  88. Vector(W, W') → w
  89. Translate(d_2, w) → e_2