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Azra Triangle

Azra Triangle
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2019-11-20 01:26
TriangleCoordinate GeometryGeometric Construction
In collections Pyramid Puzzles
This example demonstrates the construction of the Azra triangle. Key mathematical concepts include the properties of triangles and geometric construction. Using GeoGebra commands such as Polygon and Midpoint, the construction process of the triangle can be dynamically shown. Suitable for students at the junior high school level and above to learn about triangle-related knowledge.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f_5, g, h, i, C, D
  2. Polygon(D, C, 4) → poly3, n, p, q, r, G, H
  3. Polygon(H, G, 4) → poly4, s, t, a_4, b_4, I, J
  4. Polygon(J, I, 4) → poly5, c_4, d_4, e_4, f_1, K, L
  5. Polygon(L, K, 4) → poly6, g_1, h_1, i_1, j_1, M, N
  6. Polygon(N, M, 4) → poly2, j, k, l, m, E, F
  7. Midpoint(i) → O
  8. Midpoint(r) → P
  9. Midpoint(b_4) → Q
  10. Midpoint(f_1) → R
  11. Midpoint(j_1) → S
  12. Midpoint(m) → T
  13. Midpoint(m) → U
  14. Polygon(O, P, 4) → poly7, k_1, l_1, m_1, n_1, V, W
  15. Polygon(P, Q, 4) → poly8, p_1, q_1, r_1, s_1, Z, A_1
  16. Polygon(Q, R, 4) → poly9, t_1, a_1, b_1, c_1, B_1, C_1
  17. Polygon(R, S, 4) → poly10, d_1, e_1, f_2, g_2, D_1, E_1
  18. Polygon(S, T, 4) → poly11, h_2, i_2, j_2, k_2, F_1, G_1
  19. Midpoint(m_1) → H_1
  20. Midpoint(r_1) → I_1
  21. Midpoint(b_1) → J_1
  22. Polygon(H_1, I_1, 4) → poly12, l_2, m_2, n_2, p_2, K_1, L_1
  23. Polygon(I_1, J_1, 4) → poly13, q_2, r_2, s_2, t_2, M_1, N_1
  24. Midpoint(f_2) → P_1
  25. Midpoint(j_2) → Q_1
  26. Midpoint(j_2) → R_1
  27. Polygon(J_1, P_1, 4) → poly14, a_2, b_2, c_2, d_2, O_1, S_1
  28. Polygon(P_1, Q_1, 4) → poly15, e_2, f_3, g_3, h_3, T_1, U_1
  29. Midpoint(n_2) → V_1
  30. Midpoint(s_2) → W_1
  31. Midpoint(c_2) → Z_1
  32. Polygon(V_1, W_1, 4) → poly16, i_3, j_3, k_3, l_3, A_2, B_2
  33. Polygon(W_1, Z_1, 4) → poly17, m_3, n_3, p_3, q_3, C_2, D_2
  34. Midpoint(g_3) → E_2
  35. Polygon(Z_1, E_2, 4) → poly18, r_3, s_3, t_3, a_3, F_2, G_2
  36. Midpoint(k_3) → H_2
  37. Midpoint(p_3) → I_2
  38. Midpoint(t_3) → J_2
  39. Polygon(H_2, I_2, 4) → poly19, b_3, c_3, d_3, e_3, K_2, L_2
  40. Polygon(I_2, J_2, 4) → poly20, f_4, g_4, h_4, i_4, M_2, N_2
  41. Midpoint(d_3) → O_2
  42. Midpoint(h_4) → P_2
  43. Polygon(O_2, P_2, 4) → poly21, j_4, k_4, l_4, m_4, Q_2, R_2

AI Drawing Prompt Reference

Construct an Azra triangle composed of four smaller triangles. Start by using points A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z as vertices to form five large triangles, each made up of four smaller triangles. Then, find the midpoints of each large triangle to construct new smaller triangles, repeating this process until all smaller triangles are formed.
The prompt above was compiled from the original drawing commands and is for reference only.