Special Angles in Standard Position: Dynamic Templates (V2)-Part 2

Special Angles in Standard Position: Dynamic Templates (V2)-Part 2
Loading the math board and drawing, please wait…
2017-10-10 00:00
This example demonstrates the dynamic construction of 45-45-90 special right triangles in standard position. It involves core mathematical concepts like angles, trigonometry, and geometric constructions. Key GeoGebra commands and objects used include Mirror, Intersect, Dilate, Segment, Polygon, Rotate, Circle, Line, and CircleSector. Suitable for high school students learning about special right triangles and geometric constructions.

GeoGebra Commands & Parameters

  1. Mirror(G, f) → G'
  2. Mirror(F, f) → F'
  3. Mirror(E, g) → E'
  4. Mirror(F, g) → F'_1
  5. Mirror(G, g) → G'_1
  6. Mirror(F', g) → F''
  7. Mirror(G', g) → G''
  8. Mirror(E, f) → E'_1
  9. Mirror(E'_1, g) → H
  10. Intersect(g, j) → I
  11. Intersect(g, i) → J
  12. Intersect(g, h) → K
  13. Dilate(L, If[0 < a ≤ 1, 1 - a, 0], J) → L'
  14. Segment(L, L') → k
  15. Dilate(J, If[1 < a ≤ 2, 2 - a, 0], F) → K'
  16. Polygon(L, J, F) → poly1, n, e, k_1
  17. Dilate(F, If[2 < a ≤ 3, 3 - a, 0], L) → E'_2
  18. Rotate(K, If[4 < a < 5, ((-(a - 4)) * π / 3), ((-π)) / 3], E) → K'_1
  19. Rotate(K', If[4 < a < 5, ((-(a - 4)) * π / 3), ((-π)) / 3], E) → K''
  20. Rotate(L, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L'_1
  21. Rotate(K, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'_2
  22. Rotate(E, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → E'_3
  23. Rotate(K, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'_3
  24. Rotate(K', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K''_1
  25. Rotate(L, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L'_2
  26. Rotate(L', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L''
  27. Rotate(K'', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'''_1
  28. Rotate(L'_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → Q
  29. Rotate(K'_2, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → R
  30. Rotate(E'_3, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → S
  31. Rotate(K'_3, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → T
  32. Rotate(K''_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → U
  33. Rotate(L'_2, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → V
  34. Rotate(L'', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → L'''
  35. Rotate(K'''_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → W
  36. Rotate(Q, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → Q'
  37. Rotate(R, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → R'
  38. Rotate(S, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → S'
  39. Rotate(V, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → V'
  40. Rotate(L''', If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → Z
  41. Rotate(W, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → W'
  42. Rotate(T, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → T'
  43. Rotate(U, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → U'
  44. Rotate(K'_1, If[11 < a < 12, ((a - 11) * π / 6), π / 6], L) → E_1
  45. Rotate(K'', If[11 < a < 12, ((a - 11) * π / 6), π / 6], L) → K'''_2
  46. Dilate(K, If[9 < a ≤ 10, 10 - a, 0], E') → K'_4
  47. Rotate(E_1, π / 2, L) → T_1
  48. Rotate(K'''_2, π / 2, L) → U_1
  49. Rotate(K'''_2, π, L) → W_1
  50. Rotate(E_1, (3 * π / 2), L) → Z_1
  51. Rotate(K'''_2, (3 * π / 2), L) → A_2
  52. Segment(J, K') → l
  53. Segment(F, E'_2) → m
  54. Rotate(L, If[3.5 < a ≤ 4.5, ((-(a - 3.5)) * π / 2), ((-π)) / 2], J) → L'_3
  55. Rotate(L', If[3.5 < a ≤ 4.5, ((-(a - 3.5)) * π / 2), ((-π)) / 2], J) → L''_1
  56. Segment(L'_3, L''_1) → k'_1
  57. Circle(L, 0.5) → d_1
  58. Rotate(L, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L'_4
  59. Rotate(J, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → J'
  60. Rotate(F, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → F'_2
  61. Polygon(L'_4, J', F'_2) → poly1'_1, f'_2, l'_4, j'
  62. Rotate(L'_3, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → M
  63. Rotate(L''_1, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → N
  64. Segment(M, N) → b
  65. Rotate(L, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L'_5
  66. Rotate(L', If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L''_2
  67. Segment(L'_5, L''_2) → k'_3
  68. Rotate(F, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → F'_3
  69. Rotate(E'_2, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → P
  70. Segment(F'_3, P) → m'
  71. Rotate(L'_4, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → O
  72. Rotate(J', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → J''
  73. Rotate(F'_2, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → F_1
  74. Polygon(O, J'', F_1) → poly3, f_2, o, j''
  75. Rotate(M, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → M'
  76. Rotate(N, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → N'
  77. Segment(M', N') → b'
  78. Rotate(L'_5, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → G_1
  79. Rotate(L''_2, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → H_1
  80. Segment(G_1, H_1) → p
  81. Rotate(F'_3, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → I_1
  82. Rotate(P, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → P'
  83. Segment(I_1, P') → m''
  84. Rotate(O, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → O'
  85. Rotate(J'', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → J'''
  86. Rotate(F_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → J_1
  87. Polygon(O', J''', J_1) → poly3', j_2, o', j'''
  88. Rotate(M', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → M''
  89. Rotate(N', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → N''
  90. Segment(M'', N'') → b''
  91. Rotate(G_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → Q_1
  92. Rotate(H_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → R_1
  93. Segment(Q_1, R_1) → p'
  94. Rotate(I_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → S_1
  95. Rotate(P', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → P''
  96. Segment(S_1, P'') → m'''
  97. Intersect(d_1, x = 0) → B_2, C_2
  98. Line(L, F) → q
  99. Intersect(d_1, q) → D_2, E_2
  100. CircleSector(L, E_2, B_2) → r
  101. Rotate(r, If[9 < a < 10, ((-(a - 9)) * π / 4), ((-π)) / 4], L) → r'
  102. Segment(L''_2, B) → s
  103. Segment(L', A) → t
  104. Segment(D, N'') → f_1
  105. Segment(H_1, C) → g_1

AI Drawing Prompt Reference

Draw a dynamic 45-45-90 special right triangle in standard position, showing its construction process. Start by creating basic shapes through mirroring and rotation, then use similarity transformations and rotations to generate multiple triangles and polygons, and finally combine them into a complete dynamic template. The process involves angles, trigonometry, and geometric constructions, suitable for high school students.
The prompt above was compiled from the original drawing commands and is for reference only.