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HW Exercise 1.3 (#15 Constructions)

HW Exercise 1.3 (#15 Constructions)
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2017-01-25 00:16
TriangleCircleGeometric Construction
This GeoGebra example demonstrates a step-by-step geometric construction exercise, likely from a homework set, involving the creation of equilateral triangles, circles, perpendicular lines, midpoints, and other geometric elements. The core mathematical concepts include classical geometric construction rules, properties of equilateral triangles, relationships between lines and circles, and the use of perpendiculars and midpoints. The construction utilizes GeoGebra commands such as Line, Segment, Intersect, Midpoint, Circle, Point, OrthogonalLine, and Distance, along with numerous labeled objects (points, lines, circles, and text) to build the final figure. This is suitable for high school or introductory college geometry courses, helping students practice and understand the logical sequence of geometric constructions.

GeoGebra Commands & Parameters

  1. Line(A_2, B_2) → f
  2. Segment(A_2, C_2) → g
  3. Line(C_2, f) → h
  4. Line(B_2, g) → i
  5. Intersect(h, i) → D_2
  6. Segment(B_2, D_2) → j
  7. Segment(C_2, D_2) → k
  8. Segment(A_2, B_2) → l
  9. Segment(C_2, B_2) → m
  10. Segment(A_2, D_2) → n
  11. Midpoint(m) → E_2
  12. Midpoint(n) → F
  13. Segment(C_2, E_2) → p
  14. Segment(E_2, A_2) → q
  15. Segment(E_2, B_2) → r
  16. Segment(E_2, D_2) → s
  17. Segment(G, H) → t
  18. Circle(G, H) → c
  19. Point(c) → I
  20. Segment(G, I) → a
  21. Line(I, t) → b
  22. Line(H, a) → d
  23. Intersect(b, d) → J
  24. Segment(H, J) → e
  25. Segment(I, J) → f_1
  26. Segment(J, G) → g_1
  27. Segment(H, I) → h_1
  28. Midpoint(h_1) → K
  29. Midpoint(g_1) → L
  30. Segment(H, K) → i_1
  31. Segment(J, K) → j_1
  32. Segment(K, G) → k_1
  33. Segment(K, I) → l_1
  34. Segment(M, N) → m_1
  35. OrthogonalLine(M, m_1) → n_1
  36. OrthogonalLine(N, m_1) → p_1
  37. Point(n_1) → O
  38. Line(O, m_1) → q_1
  39. Intersect(p_1, q_1) → P
  40. Segment(O, P) → r_1
  41. Segment(M, O) → s_1
  42. Segment(N, P) → t_1
  43. Segment(M, P) → a_1
  44. Segment(N, O) → b_1
  45. Midpoint(a_1) → Q
  46. Midpoint(b_1) → R
  47. Segment(M, Q) → c_1
  48. Segment(O, Q) → d_1
  49. Segment(Q, N) → e_1
  50. Segment(Q, P) → f_2
  51. Segment(S, T) → g_2
  52. Circle(S, T) → c_2
  53. OrthogonalLine(S, g_2) → h_2
  54. OrthogonalLine(T, g_2) → i_2
  55. Intersect(c_2, h_2, 2) → U
  56. Line(U, g_2) → j_2
  57. Intersect(i_2, j_2) → V
  58. Segment(U, V) → k_2
  59. Segment(V, T) → l_2
  60. Segment(S, U) → m_2
  61. Segment(T, U) → n_2
  62. Segment(S, V) → p_2
  63. Midpoint(n_2) → W
  64. Midpoint(p_2) → Z
  65. Segment(T, W) → q_2
  66. Segment(W, V) → r_2
  67. Segment(W, S) → s_2
  68. Segment(W, U) → t_2
  69. Circle(A, B) → d_2
  70. Point(d_2) → C
  71. Point(d_2) → D
  72. Point(d_2) → E
  73. Segment(C, B) → a_2
  74. Segment(C, D) → b_2
  75. Segment(D, E) → e_2
  76. Segment(E, B) → f_3
  77. Segment(C, E) → g_3
  78. Segment(D, B) → h_3
  79. Intersect(g_3, h_3) → A_1
  80. Segment(D, A_1) → i_3
  81. Segment(C, A_1) → j_3
  82. Segment(A_1, B) → k_3
  83. Segment(A_1, E) → l_3
  84. Distance(j_3, k_3) → o