MathPlotAI Logo MathPlotAI

Dynamic Exploration of Triangle Area

Dynamic Exploration of Triangle Area
Loading the math board and drawing, please wait…
2021-11-05 08:28
TriangleAngleGeometric Construction
In collections Visual Geometry for Grade 9
This example demonstrates how to dynamically explore the area calculation of a triangle. Key math concepts involved include the formula for the area of a triangle, angles, similarity transformations, and vectors. Construction highlights use GeoGebra commands and objects such as Rotate, Angle, Ray, Segment, Intersect, Midpoint, Line, OrthogonalLine, Polygon, Point, Circle, Dilate, Min, CircleSector, Vector, and Translate. Suitable for middle school and above students to understand triangle area calculation and geometric transformations.

GeoGebra Commands & Parameters

  1. Rotate(A, α, B) → A'
  2. Angle(A, B, A') → γ
  3. Ray(B, A') → f
  4. Rotate(B, (-β), A) → B'
  5. Angle(B', A, B) → δ
  6. Ray(A, B') → g
  7. Segment(B, A) → h
  8. Intersect(f, g) → C
  9. Segment(B, C) → i
  10. Segment(A, C) → j
  11. Midpoint(i) → D
  12. Midpoint(j) → E
  13. Line(B, A) → l
  14. OrthogonalLine(C, l) → m
  15. Intersect(l, m) → F
  16. Segment(C, F) → n
  17. Polygon(D, E, C) → poly1, c, d, e
  18. Midpoint(n) → G
  19. Line(C, l) → p
  20. Polygon(B, D, E, A) → poly2, b, d_1, e_1, a
  21. Segment(D, C) → q
  22. Segment(B, A) → r
  23. Point(p) → H
  24. OrthogonalLine(H, p) → t
  25. Intersect(l, t) → I
  26. Segment(H, I) → s
  27. Circle(I, 3) → c_1
  28. Circle(H, 3) → f_1
  29. Intersect(f_1, p, 1) → J
  30. Intersect(f_1, p, 2) → K
  31. Intersect(c_1, l, 2) → L
  32. Intersect(c_1, s, 1) → M
  33. Intersect(c_1, l, 1) → N
  34. Angle(J, H, I) → ε
  35. Angle(M, I, N) → ζ
  36. Dilate(H, If[0 < k ≤ 1, 1 - k, 0], I) → H'
  37. Segment(H, H') → g_1
  38. Angle(C, F, B) → η
  39. Dilate(C, If[1 < k ≤ 2, 2 - k, 0], G) → C'
  40. Segment(C, C') → h_1
  41. Dilate(G, If[2 < k ≤ 3, 3 - k, 0], F) → G'
  42. Segment(G, G') → i_1
  43. Rotate(C, If[3 < k ≤ 4, ((-(k - 3)) * π), (-π)], G) → C'_1
  44. Rotate(C', If[3 < k ≤ 4, ((-(k - 3)) * π), (-π)], G) → C''
  45. Segment(C'_1, C'') → j_1
  46. Dilate(G, If[4 < k ≤ 5, 5 - k, 0], D) → G'_1
  47. Dilate(G, If[4 < k ≤ 5, 5 - k, 0], E) → G'_2
  48. Segment(G, G'_1) → k_1
  49. Segment(G, G'_2) → l_1
  50. Segment(B, F) → m_1
  51. Segment(B, D) → n_1
  52. Segment(D, G) → p_1
  53. Segment(D, C) → q_1
  54. Min({m_1, n_1, p_1, q_1}) → o
  55. Circle(B, (0.6 * o)) → r_1
  56. Intersect(r_1, l) → O, P
  57. Segment(B, C) → s_1
  58. Intersect(r_1, s_1, 1) → Q
  59. CircleSector(B, P, Q) → t_1
  60. Rotate(D, If[6 < k ≤ 7, ((-(k - 6)) * π), (-π)], E) → D'
  61. Rotate(E, If[6 < k ≤ 7, ((-(k - 6)) * π), (-π)], E) → E'
  62. Rotate(C, If[6 < k ≤ 7, ((-(k - 6)) * π), (-π)], E) → C'_2
  63. Polygon(D', E', C'_2) → poly1', c'_2, d', e'
  64. Segment(D, C) → a_1
  65. Segment(D, B) → b_1
  66. Segment(C, E) → f_2
  67. Segment(E, A) → g_2
  68. Segment(E, C'_2) → h_2
  69. Segment(C'_2, D') → i_2
  70. Segment(D', E) → j_2
  71. Dilate(D, If[7 < k ≤ 8, 8 - k, 0], C) → D'_1
  72. Segment(D, D'_1) → k_2
  73. Dilate(B, If[8 < k ≤ 9, 9 - k, 0], D) → B'_1
  74. Vector(B, B'_1) → u
  75. Translate(t_1, u) → c_2
  76. Dilate(B, If[9 < k ≤ 10, 10 - k, 0], A) → B'_2
  77. Vector(B, B'_2) → v
  78. Translate(t_1, v) → d_2
  79. Circle(A, Radius[r_1]) → e_2
  80. Intersect(e_2, l, 1) → R
  81. Intersect(e_2, g_2, 1) → S
  82. Segment(B, A) → l_2
  83. Segment(A, C) → m_2
  84. Min({l_2, m_2}) → w
  85. Circle(A, (0.25 * w)) → p_2
  86. Intersect(g_2, m_2) → T
  87. Intersect(g_2, m_2) → U
  88. Intersect(p_2, m_2) → V,
  89. Intersect(p_2, l_2) → W,
  90. CircleSector(A, V, W) → q_2

AI Drawing Prompt Reference

Draw triangle ABC, use rotation and angle calculations to find the height and midpoints, construct medians and perpendicular bisectors, apply similarity transformations and rotations to explore the area of the triangle dynamically, and finally use circle intersections and rotations to create dynamic effects.
The prompt above was compiled from the original drawing commands and is for reference only.