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Sec 1.6 Basic Constructions：Basic Geometric Constructions

Sec 1.6 Basic Constructions：Basic Geometric Constructions
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2015-09-25 00:40
Coordinate GeometryTransformationGeometric Construction
This example demonstrates basic geometric constructions using GeoGebra, including triangles, circles, polygons, and angles. Key mathematical concepts involve geometric construction, coordinate geometry, and transformations. The construction uses commands like Segment, Rotate, Angle, Circle, Intersect, and objects such as Point, Vector, Ellipse. Suitable for middle or high school mathematics to understand geometric construction principles and practical applications.

GeoGebra Commands & Parameters

  1. Segment(A_1, B_1) → a
  2. Segment(X_1, Y_1) → b
  3. Rotate(C_1, 32*°, B_2) → A_2
  4. Angle(C_1, B_2, A_2) → α
  5. Segment(B_2, A_2) → c
  6. Segment(B_2, C_1) → d
  7. Rotate(C_2, 45*°, B_3) → A_3
  8. Angle(C_2, B_3, A_3) → β
  9. Segment(B_3, A_3) → e
  10. Segment(B_3, C_2) → f
  11. Segment(A_4, B_4) → g
  12. Rotate(D_1, 60*°, A) → D'
  13. Angle(D_1, A, D') → γ
  14. Segment(A, D') → h
  15. Segment(A, D_1) → i
  16. Rotate(Z, 120*°, Y_2) → X_2
  17. Angle(Z, Y_2, X_2) → δ
  18. Segment(X_2, Y_2) → j
  19. Segment(Y_2, Z) → k
  20. Point(g) → E
  21. Circle(A_4, Segment[A_4, E]) → p
  22. Circle(B_4, Segment[A_4, E]) → q
  23. Intersect(p, q, 1) → X
  24. Intersect(p, q, 2) → Y
  25. Segment(Y, X) → l
  26. Intersect(g, l) → C_3
  27. Angle(B_4, C_3, X) → ε
  28. Angle(X, C_3, B_4) → ζ
  29. Segment(S, T) → m
  30. Point(m) → F
  31. Circle(S, Segment[S, F]) → r
  32. Circle(T, Segment[S, F]) → s
  33. Intersect(r, s, 1) → G
  34. Intersect(r, s, 2) → H
  35. Segment(H, G) → n
  36. Intersect(m, n) → I
  37. Point(m) → J
  38. Circle(S, Segment[S, J]) → t
  39. Circle(I, Segment[S, J]) → c_1
  40. Intersect(t, c_1, 1) → K
  41. Intersect(t, c_1, 2) → L
  42. Segment(K, L) → a_1
  43. Intersect(m, a_1) → M
  44. Point(h) → B
  45. Circle(A, Segment[B, A]) → d_1
  46. Intersect(d_1, i, 1) → C
  47. Circle(B, Segment[B, C]) → e_1
  48. Circle(C, Segment[B, C]) → f_1
  49. Intersect(e_1, f_1, 1) → D
  50. Vector(A, N) → u
  51. Angle(C, A, D) → η
  52. Angle(D, A, B) → θ
  53. Point(j) → O
  54. Circle(P, Q) → g_1
  55. Circle(P, R) → h_1
  56. Circle(P, U) → k_1
  57. Circle(P, V) → p_1
  58. Circle(P, W) → q_1
  59. Circle(P, E_1) → r_1
  60. Circle(P, F_1) → s_1
  61. Circle(P, G_1) → t_1
  62. Circle(P, H_1) → c_2
  63. Circle(P, I_1) → d_2
  64. Circle(P, J_1) → e_2
  65. Circle(P, K_1) → f_2
  66. Circle(P, L_1) → g_2
  67. Circle(M_1, N_1) → h_2
  68. Ellipse(O_1, P_1, Q_1) → k_2
  69. Ellipse(R_1, S_1, T_1) → p_2
  70. Ellipse(U_1, V_1, W_1) → q_2
  71. Ellipse(Z_1, R_1, D_2) → r_2