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Dynamic Triangle Area Exploration

Dynamic Triangle Area Exploration
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2017-01-23 05:47
TriangleAngleVectorGeometric ConstructionSlider Animation
In collections Congruence (CO) Cluster CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Perimeter & Area Area
This example demonstrates how to dynamically calculate and modify the area of a triangle. Key math concepts include triangle area formulas, dynamic geometric transformations, and angle calculations. Construction highlights involve commands like Rotate, Angle, Segment, Intersect, Midpoint, Line, OrthogonalLine, Polygon, Point, Circle, Dilate, Min, CircleSector, Vector, and Translate in GeoGebra. It is suitable for high school mathematics education, exploring the relationship between triangle area, side lengths, and angles to deepen understanding of area formulas.

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