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2014-05-01 23:14
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the concept of similar figures. By using transformations such as dilation and rotation, you can observe the properties of similar figures. The construction involves commands like Polygon, Midpoint, Segment, etc. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(a) → D
  3. Midpoint(b) → E
  4. Midpoint(c) → F
  5. Segment(F, C) → d
  6. Segment(E, B) → e
  7. Intersect(d, e) → G
  8. Mirror(G, a) → G'
  9. Line(G', a) → f
  10. OrthogonalLine(D, a) → g
  11. Intersect(g, f) → H
  12. Ray(D, H) → h
  13. Point(h) → I
  14. Line(I, a) → i
  15. Segment(D, I) → j
  16. OrthogonalLine(F, c) → k
  17. OrthogonalLine(E, b) → l
  18. Circle(F, j) → p
  19. Circle(E, j) → q
  20. Intersect(p, k, 1) → J
  21. Intersect(q, l, 1) → K
  22. Line(J, c) → m
  23. Line(K, b) → n
  24. Intersect(m, n) → L
  25. Intersect(i, n) → M
  26. Intersect(i, m) → N
  27. Segment(F, J) → r
  28. Segment(E, K) → s
  29. Polygon(L, N, M) → poly2, m_1, l_1, n_1
  30. Polygon(O, P, Q, R) → poly3, o, p_1, q_1, r_1
  31. Segment(R, P) → t
  32. Segment(O, Q) → a_1
  33. Intersect(t, a_1) → S
  34. Midpoint(p_1) → T
  35. Midpoint(q_1) → U
  36. Midpoint(r_1) → V
  37. Midpoint(o) → W
  38. Mirror(S, p_1) → S'
  39. Line(S', p_1) → b_1
  40. OrthogonalLine(T, b_1) → c_1
  41. Intersect(b_1, c_1) → Z
  42. Ray(T, Z) → d_1
  43. Point(d_1) → A_1
  44. Line(A_1, p_1) → e_1
  45. Segment(T, A_1) → f_1
  46. OrthogonalLine(W, o) → g_1
  47. Circle(W, f_1) → h_1
  48. Intersect(h_1, g_1, 1) → B_1
  49. Line(B_1, o) → i_1
  50. Segment(W, B_1) → j_1
  51. Intersect(e_1, i_1) → C_1
  52. OrthogonalLine(V, r_1) → k_1
  53. Circle(V, f_1) → s_1
  54. Intersect(s_1, k_1, 1) → D_1
  55. Line(D_1, r_1) → t_1
  56. Segment(V, D_1) → a_2
  57. Intersect(i_1, t_1) → E_1
  58. OrthogonalLine(U, q_1) → b_2
  59. Circle(U, f_1) → c_2
  60. Intersect(c_2, b_2, 1) → F_1
  61. Line(F_1, q_1) → d_2
  62. Segment(U, F_1) → e_2
  63. Intersect(t_1, d_2) → G_1
  64. Intersect(e_1, d_2) → H_1
  65. Polygon(E_1, C_1, H_1, G_1) → poly4, e_3, c_3, h_2, g_2

AI Drawing Prompt Reference

Draw two similar triangles. First, draw triangle ABC. Then, use midpoints D, E, and F to construct segments and mirrors. Next, use perpendicular lines and circles to find corresponding points for the similar triangle. Finally, use mirrors and perpendicular lines to construct the second triangle, ensuring both triangles are similar.
The prompt above was compiled from the original drawing commands and is for reference only.