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Geometric Properties of Quadrilaterals

Geometric Properties of Quadrilaterals
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2017-12-11 13:45
AngleGeometric Construction
In collections Mathematics Form 1
This example demonstrates the geometric properties and relationships of various quadrilaterals (kites, parallelograms, rectangles, squares, trapezoids). It covers core concepts like diagonals, angle sums, side relationships, symmetry, and area calculations. The construction uses commands such as Segment, Rotate, Distance, Angle, OrthogonalLine, Point, Line, Intersect, Circle, LineBisector, and Ray. Ideal for high school mathematics instruction or exploration by geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Rotate(A, (-(90°)), B) → C
  3. Rotate(B, 90°, A) → D
  4. Segment(D, A) → b
  5. Segment(D, C) → c
  6. Segment(C, B) → d
  7. Distance(A, B) → AB
  8. Angle(B, A, D) → α
  9. Angle(A, D, C) → β
  10. Angle(D, C, B) → γ
  11. Angle(C, B, A) → δ
  12. Segment(E, F) → f
  13. OrthogonalLine(E, f) → g
  14. OrthogonalLine(F, f) → h
  15. Point(g) → G
  16. Line(G, f) → i
  17. Intersect(h, i) → H
  18. Segment(E, G) → j
  19. Segment(G, H) → k
  20. Segment(H, F) → l
  21. Angle(F, E, G) → ε
  22. Angle(E, G, H) → ζ
  23. Angle(G, H, F) → η
  24. Angle(H, F, E) → θ
  25. Distance(E, F) → EF
  26. Distance(E, G) → EG
  27. Circle(I, J) → p
  28. Segment(I, J) → n
  29. Point(p) → K
  30. Segment(I, K) → q
  31. Line(K, n) → r
  32. Line(J, q) → s
  33. Intersect(r, s) → L
  34. Segment(K, L) → t
  35. Segment(J, L) → a_1
  36. Distance(I, J) → IJ
  37. Distance(I, K) → IK
  38. Line(M, q) → b_1
  39. Line(M, t) → c_1
  40. Segment(N, O) → d_1
  41. Segment(N, P) → e_1
  42. Line(P, d_1) → f_1
  43. Line(O, e_1) → g_1
  44. Intersect(f_1, g_1) → Q
  45. Segment(P, Q) → h_1
  46. Segment(Q, O) → i_1
  47. Distance(N, O) → NO
  48. Distance(N, P) → NP
  49. Line(R, e_1) → j_1
  50. Line(R, h_1) → k_1
  51. Segment(S, T) → l_1
  52. Line(U, l_1) → m_1
  53. Point(m_1) → V
  54. Segment(U, S) → n_1
  55. Segment(V, T) → p_1
  56. Segment(U, V) → q_1
  57. Segment(A_2, A_4) → r_1
  58. LineBisector(A_4, A_2) → s_1
  59. Intersect(s_1, r_1) → W
  60. Point(s_1) → Z
  61. Ray(W, Z) → d_2
  62. Point(s_1) → B_1
  63. Ray(W, B_1) → e_2
  64. Point(e_2) → A_3
  65. Point(d_2) → A_1
  66. Segment(A_4, A_3) → t_1
  67. Segment(A_3, A_2) → a_2
  68. Segment(A_2, A_1) → b_2
  69. Segment(A_1, A_4) → c_2
  70. Distance(A_1, A_2) → A1A2
  71. Distance(A_1, A_4) → A1A4
  72. Distance(A_2, A_3) → A2A3
  73. Distance(A_4, A_3) → A3A4
  74. Segment(A, C) → f_2
  75. Segment(D, B) → g_2
  76. Intersect(f_2, g_2) → C_1
  77. Angle(C, C_1, D) → ι
  78. Distance(A, C_1) → AC01
  79. Distance(C, C_1) → CC01
  80. Distance(D, C_1) → DC01
  81. Distance(B, C_1) → BC01
  82. Segment(E, H) → h_2
  83. Segment(G, F) → i_2
  84. Intersect(h_2, i_2) → D_1
  85. Distance(E, D_1) → ED01
  86. Distance(F, D_1) → FD01
  87. Distance(G, D_1) → GD01
  88. Distance(H, D_1) → HD01
  89. Segment(I, L) → j_2
  90. Segment(J, K) → k_2
  91. Intersect(j_2, k_2) → E_1
  92. Angle(L, E_1, K) → κ
  93. Distance(I, E_1) → IE01
  94. Distance(J, E_1) → JE01
  95. Distance(K, E_1) → KE01
  96. Distance(L, E_1) → LE01
  97. Segment(N, Q) → l_2
  98. Segment(O, P) → m_2
  99. Intersect(l_2, m_2) → F_1
  100. Distance(N, F_1) → NF01
  101. Distance(O, F_1) → OF01
  102. Distance(P, F_1) → PF01
  103. Distance(Q, F_1) → QF01
  104. Segment(A_3, A_1) → n_2
  105. Angle(r_1, n_2) → λ
  106. Intersect(r_1, n_2) → G_1
  107. Distance(A_1, G_1) → A02G01
  108. Distance(A_4, G_1) → A04G01
  109. SelectedIndex(Bahasa) → nn
  110. If(nn ≟ 1, "units", "unit") → UTex