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Making Squares

Making Squares
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2017-01-20 09:04
AngleTransformationGeometric Construction
This example demonstrates how to create squares using GeoGebra. Key mathematical concepts include geometric construction, angles, and transformations. Commands such as Circle, Intersect, Polygon, Segment, Rotate, Line, Point, Angle, Sequence, and AngularBisector are used to construct the square. Suitable for middle school and above students to learn geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Circle(G, leg1) → c
  2. Intersect(c, f, 2) → B'
  3. Circle(G, leg2) → d
  4. Intersect(d, g, 1) → C'
  5. Circle(C', leg2) → e
  6. Polygon(G, B', C') → polyG, c', a', b'
  7. Circle(F, leg2) → k
  8. Intersect(k, m) → B_2, C_1
  9. Intersect(n, p) → D_2
  10. Circle(D_2, leg2 - leg1) → r
  11. Intersect(r, p, 1) → E_2
  12. Circle(D_2, leg1) → s
  13. Intersect(s, n, 1) → F_2
  14. Intersect(q, p) → G_1
  15. Segment(F, E_2) → t_3
  16. Rotate(F, (-(90°)), E_2) → A'_1
  17. Line(E_2, A'_1) → a
  18. Intersect(n, a) → H_1
  19. Polygon(F, C_1, H_1, E_2) → polyF, a_1, c_1, h_1, e_1
  20. Circle(E, leg1) → d_1
  21. Intersect(d_1, b, 2) → J
  22. Circle(E, leg1^(2) / leg2) → k_1
  23. Intersect(k_1, g_1, 2) → K
  24. Polygon(E, J, K) → polyE, k_2, i_1, j_1
  25. Circle(H, leg1) → t_1
  26. Intersect(t_1, r_1, 2) → P
  27. Circle(H, leg1 - leg1^(2) / leg2) → c_2
  28. Intersect(c_2, s_1, 1) → Q
  29. Intersect(b_1, f_2) → R
  30. Polygon(H, P, R, Q) → polyH, o, p_2, r_2, q_2
  31. Circle(D, leg2 - leg1) → d_2
  32. Intersect(d_2, g_2, 2) → T
  33. Circle(T, leg1 - leg1^(2) / leg2) → e_2
  34. Intersect(e_2, h_2, 1) → U
  35. Polygon(D, T, U) → polyD, u_1, s_2, t_2
  36. Point(Circle[B, leg2]) → M
  37. Segment(B, M) → l_1
  38. Polygon(B, M, 4) → polyB, m_1, n_1, p_1, q_1, N, V
  39. Point(Circle[A, leg1]) → Z
  40. Segment(A, Z) → i_2
  41. Polygon(A, Z, 4) → polyA, j_2, l_2, m_2, n_2, A_1, B_1
  42. Point(Circle[C, sqrt(leg1^(2) + leg2^(2))]) → D_1
  43. Segment(C, D_1) → a_2
  44. Polygon(C, D_1, 4) → polyC, b_2, f_3, g_3, h_3, E_1, F_1
  45. Angle(polyG) → α, β, γ
  46. Sequence(Segment[(x(B), y(B) + w), (x(B) + leg2, y(B) + w)], w, 0, leg2) → list2
  47. Sequence(Segment[(x(B) + w, y(B)), (x(B) + w, y(B) + leg2)], w, 0, leg2) → list5
  48. Sequence(Segment[(x(A), y(A) + w), (x(A) + leg1, y(A) + w)], w, 0, leg1) → list3
  49. Sequence(Segment[(x(A) + w, y(A)), (x(A) + w, y(A) + leg1)], w, 0, leg1) → list6
  50. Sequence(Segment[(x(C), y(C) + w), (x(C) + hyp, y(C) + w)], w, 0, hyp) → list1
  51. Sequence(Segment[(x(C) + w, y(C)), (x(C) + w, y(C) + hyp)], w, 0, hyp) → list4
  52. Rotate(polyC, ε, C) → polyC'
  53. Rotate(list1, ε, C) → list1'
  54. Rotate(list4, ε, C) → list4'
  55. AngularBisector(F, C_1, H_1) → i_3
  56. AngularBisector(F, E_2, C_1) → j_3
  57. Intersect(i_3, j_3) → I
  58. AngularBisector(E, J, K) → k_3
  59. AngularBisector(K, E, J) → l_3
  60. AngularBisector(J, K, E) → m_3
  61. Intersect(k_3, l_3) → L
  62. AngularBisector(C', G, B') → n_3
  63. AngularBisector(B', C', G) → p_3
  64. Intersect(n_3, p_3) → O
  65. AngularBisector(P, H, Q) → q_3
  66. AngularBisector(H, P, R) → r_3
  67. AngularBisector(H, Q, R) → s_3
  68. AngularBisector(Q, R, P) → a_3
  69. Intersect(r_3, a_3) → S
  70. AngularBisector(D, T, U) → b_3
  71. AngularBisector(U, D, T) → c_3
  72. Intersect(b_3, c_3) → W