Special Right Triangles Game

Special Right Triangles Game
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2016-05-23 09:28
This example demonstrates the construction and properties of special right triangles (30°-60°-90° and 45°-45°-90°). It involves core mathematical concepts including right triangles, trigonometry, ratios, fractions, and geometric transformations. The construction utilizes commands and objects such as Segment, Point, Midpoint, Rotate, Line, Intersect, Mirror, Polygon, Angle, Textfield, OrthogonalLine, Element, LaTeX in GeoGebra. Suitable for middle school and above students to understand and apply geometric and trigonometric knowledge of special right triangles.

GeoGebra Commands & Parameters

  1. Segment(B, A) → d
  2. Segment(C, B) → p
  3. Segment(D, A) → k
  4. Point(k) → F
  5. Midpoint(D, F) → M
  6. Rotate(D, 90*°, M) → D'
  7. Line(D', p) → g_1
  8. Segment(C, D) → r
  9. Intersect(g_1, r) → P
  10. Mirror(P, D') → P'
  11. Segment(D', P') → k_1
  12. Midpoint(B, A) → I
  13. Midpoint(B, I) → J
  14. Line(J, p) → s
  15. Intersect(r, s) → G
  16. Midpoint(G, J) → N
  17. Segment(N, J) → i_1
  18. Line(B, yAxis) → e
  19. Line(A, yAxis) → f
  20. Segment(C, B) → j
  21. Point(j) → E
  22. Polygon(E, B, A) → poly1, a_1, e_1, b_1
  23. Polygon(F, B, A) → poly2, a_2, f_1, b_2
  24. Angle(A, B, F) → α
  25. Angle(B, F, A) → β
  26. Angle(B, E, A) → γ
  27. Angle(E, A, B) → δ
  28. Angle(A, B, E) → ε
  29. Angle(F, A, B) → ζ
  30. Segment(D, A) → q
  31. Midpoint(I, A) → K
  32. Line(K, s) → t
  33. Intersect(r, t) → H
  34. Segment(G, J) → c_1
  35. Point(i_1) → L
  36. Polygon(L, A, D) → poly3, d_1, l_1, a_3
  37. Angle(L, D, A) → η
  38. Angle(D, A, L) → θ
  39. Segment(P, P') → h_1
  40. Point(k_1) → Q
  41. Polygon(Q, D, F) → poly4, f_2, q_1, d_2
  42. Angle(Q, D, A) → ι
  43. Angle(D, A, Q) → κ
  44. Segment(D', Q) → j_1
  45. Midpoint(H, K) → S
  46. Segment(S, K) → m_1
  47. Point(m_1) → T
  48. Polygon(C, T, B) → poly5, b_3, c_2, t_1
  49. Angle(B, C, T) → λ
  50. Angle(T, B, C) → μ
  51. Midpoint(S, M) → U
  52. Midpoint(K, A) → V
  53. Segment(U, V) → n_1
  54. Point(n_1) → W
  55. Polygon(C, W, B) → poly6, b_4, c_3, w
  56. Angle(W, B, C) → ν
  57. Angle(B, C, W) → ξ
  58. Segment(L, A) → p_1
  59. Segment(A, D) → r_1
  60. Segment(L, D) → s_1
  61. Segment(L, A) → e_2
  62. Segment(L, D) → g_2
  63. Segment(A, D) → h_2
  64. Segment(C, T) → i_2
  65. Segment(T, B) → j_2
  66. Segment(C, B) → k_2
  67. Segment(C, T) → l_2
  68. Segment(T, B) → m_2
  69. Segment(C, B) → n_2
  70. Segment(Q, D) → p_2
  71. Segment(D, F) → q_2
  72. Segment(Q, F) → r_2
  73. Segment(Q, D) → s_2
  74. Segment(D, F) → t_2
  75. Segment(Q, F) → d_3
  76. Segment(C, W) → e_3
  77. Segment(W, B) → f_3
  78. Segment(C, B) → g_3
  79. Segment(C, W) → h_3
  80. Segment(W, B) → i_3
  81. Segment(C, B) → j_3
  82. Textfield(text1) → inputBox1
  83. Textfield(Work) → inputBox2
  84. Line(A, L) → k_3
  85. OrthogonalLine(L, k_3) → l_3
  86. Point(l_3) → Z
  87. Element(answer, Problem) → m_3
  88. Angle(A, L, D) → ο
  89. Angle(A, L, D) → ρ
  90. Angle(A, L, D) → σ
  91. Angle(F, Q, D) → τ
  92. Angle(F, Q, D) → υ
  93. Angle(F, Q, D) → ϕ
  94. Angle(C, T, B) → χ
  95. Angle(C, T, B) → ψ
  96. Angle(C, T, B) → ω
  97. Angle(C, W, B) → α_1
  98. Angle(C, W, B) → β_1
  99. Angle(C, W, B) → γ_1
  100. Element(angle, Problem) → δ_1
  101. LaTeX(right, true, true) → text3
  102. LaTeX(wrong, true, true) → text4
  103. Textfield(Name) → inputBox3
  104. Textfield(Date) → inputBox4
  105. Segment(C_1, D_1) → n_3
  106. Point(n_3) → E_1
  107. Ellipse(A_1, B_1, E_1) → p_3
  108. Mirror(B, A) → B'
  109. Ellipse(C, B', E_1) → q_3
  110. Point(q_3) → F_1
  111. Point(q_3) → G_1

AI Drawing Prompt Reference

Draw a geometric diagram showing the construction and properties of 30°-60°-90° and 45°-45°-90° special right triangles. Start by drawing two right triangles, then use rotation, reflection, and connection to construct new shapes. Label key points, segments, and midpoints, and display angles and text to help understand the side length ratios and angle relationships of the triangles.
The prompt above was compiled from the original drawing commands and is for reference only.