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Rotation and Equilateral Triangle

Rotation and Equilateral Triangle
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2020-03-11 21:36
TriangleAngleFunctionGeometric Construction
This example demonstrates the rotation of an equilateral triangle and its related properties. Key mathematical concepts include angles, rotation, equilateral triangles, and functions. Using GeoGebra commands such as Rotate, Polygon, and Angle, a dynamic model of the rotating equilateral triangle can be constructed. Suitable for middle school and above students to learn geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. Rotate(A, β, B) → C
  2. Angle(C, B, A) → δ
  3. Rotate(C, ζ, A) → A''
  4. Angle(A'', A, C) → η
  5. Rotate(B, θ, C) → B'
  6. Angle(B', C, B) → ι
  7. Segment(C, A) → f
  8. Segment(A, B) → g
  9. Segment(C, B) → h
  10. Segment(A, B') → i
  11. Polygon(G, H, I) → t1, i_1, g_1, h_1
  12. Polygon(J, K, L) → t2, l, j, k
  13. Segment(M, D) → m
  14. Segment(D, E) → n
  15. Segment(E, F) → p
  16. Segment(F, M) → q
  17. Point(k) → N
  18. Circle(N, O) → c
  19. Segment(P, Q) → r
  20. Circle(R, 3.5206630456888095) → d
  21. Circle(V, 4.318008404361196) → s
  22. Ellipse(W, Z, A_1) → e
  23. Circle(B_1, 1.1986867356097015) → t
  24. Circle(C_1, 1.157712222355001) → c_1
  25. Circle(D_1, 1.5782890280556081) → d_1
  26. Circle(E_1, 1.0245749186240654) → e_1
  27. Ellipse(F_1, G_1, H_1) → f_1
  28. Circle(I_1, 0.7286722651827102) → k_1
  29. Ellipse(M_1, N_1, O_1) → q_1
  30. Circle(V_1, 0.8290493702679644) → t_1
  31. Circle(W_1, 1.2121144859053594) → c_2
  32. Polygon(C_2, D_2, E_2) → t3, e_2, a, d_2
  33. Polygon(F_2, G_2, H_2, I_2) → q1, f_2, g_2, h_2, i_2
  34. Polygon(J_2, K_2, L_2, M_2) → q2, j_2, k_2, l_2, m_2

AI Drawing Prompt Reference

Draw an equilateral triangle and show its rotation around a vertex. Start with the initial triangle, then rotate each vertex sequentially to form multiple rotated triangles, marking the rotation angles. Connect corresponding vertices before and after rotation with auxiliary segments. Add several circles, ellipses, and auxiliary polygons around the figure to illustrate rotational symmetry and geometric relationships. The overall composition includes multiple triangles, circles, ellipses, and segments, emphasizing angle changes and visual effects of transformation.
The prompt above was compiled from the original drawing commands and is for reference only.