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Quadrilateral Interior Angles

Quadrilateral Interior Angles
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2017-12-11 13:38
PolygonAngleGeometric Construction
In collections Mathematics Form 1
This example demonstrates the calculation and properties of interior angles in a quadrilateral. It involves core mathematical concepts such as the sum of interior angles theorem and polygon geometry. Construction highlights include using GeoGebra commands like Circle, Segment, Intersect, Line, and Angle to build the quadrilateral and measure its interior angles. Suitable for middle school and above students learning about polygon angle properties and geometric constructions.

GeoGebra Commands & Parameters

  1. Circle(Q, Saiz) → h_1
  2. Segment(P, Q) → a_1
  3. Intersect(h_1, a_1, 1) → Q_2
  4. Segment(P, S) → c_1
  5. Line(Q, c_1) → d_1
  6. Intersect(h_1, d_1, 2) → Q_1
  7. Angle(Q_1, Q, Q_2) → θ
  8. If(θ < 180°, CircleSector[Q, Q_1, Q_2], CircleSector[Q, Q_2, Q_1]) → k_1
  9. If(o < 1, 1, o) → T_2
  10. If(o > 1, 1, o) → T_1
  11. Circle(P, Saiz) → e_1
  12. Intersect(e_1, c_1, 1) → P_2
  13. Intersect(e_1, a_1, 1) → P_1
  14. Angle(P_1, P, P_2) → ε
  15. If(ε < 180°, CircleSector[P, P_1, P_2], CircleSector[P, P_2, P_1]) → p_1
  16. Circle(C, Saiz) → h
  17. Line(B, C) → m_0
  18. Intersect(h, m_0, 1) → C_2
  19. Segment(C, D) → c
  20. Intersect(h, c, 1) → C_1
  21. Segment(D, A) → d
  22. Circle(D, Saiz) → k
  23. Intersect(k, d, 1) → D_1
  24. Intersect(k, c, 1) → D_2
  25. Circle(B, Saiz) → g
  26. Intersect(g, m_0, 2) → B_2
  27. Segment(A, B) → a
  28. Intersect(g, a, 1) → B_1
  29. If(m_2 < 1, 1, m_2) → S_3
  30. If(m_2 > 1, 1, m_2) → S_4
  31. Segment(B, C) → b
  32. Point(m_0) → E
  33. Circle(A, Saiz) → f
  34. Intersect(f, a, 1) → A_1
  35. Intersect(f, d, 1) → A_2
  36. Line(D, yAxis) → l
  37. Segment(C, E) → i
  38. CircleSector(D, D_1, D_2) → q
  39. Rotate(q, (((-S_4) * 180))°, D) → q'
  40. Vector(D, A) → u_1
  41. Vector(B, A) → u_2
  42. CircleSector(B, B_2, B_1) → s
  43. Rotate(s, (((S_3 - 1) * 180))°, B) → s'
  44. Vector(C, A) → u_3
  45. If(m_2 < 0.5, 0.5, If[m_2 > 1.5, 1.5, m_2]) → S_5
  46. Translate(q', Vector[(S_4 * u_1)]) → q''
  47. CircleSector(C, C_1, C_2) → p
  48. Translate(p, Vector[((S_5 - 0.5) * u_3)]) → p'
  49. Translate(s', Vector[((S_3 - 1) * u_2)]) → s''
  50. Intersect(h, i, 1) → C_3
  51. CircleSector(C, C_3, C_1) → t
  52. Line(S, a_1) → b_1
  53. Intersect(b_1, d_1) → R
  54. Circle(S, Saiz) → f_1
  55. Circle(R, Saiz) → g_1
  56. Intersect(f_1, c_1, 1) → S_1
  57. Intersect(f_1, b_1, 2) → S_2
  58. Intersect(g_1, b_1, 1) → R_1
  59. Intersect(g_1, d_1, 1) → R_2
  60. Angle(S_1, S, S_2) → ζ
  61. Angle(R_1, R, R_2) → η
  62. If(ζ < 180°, CircleSector[S, S_1, S_2], CircleSector[S, S_2, S_1]) → q_1
  63. If(η < 180°, CircleSector[R, R_1, R_2], CircleSector[R, R_2, R_1]) → r_1
  64. Vector(Q, S) → v_1
  65. Vector(P, R) → v_2
  66. Rotate(p_1, ((T_1 * 180))°, P) → t_1
  67. Translate(t_1, Vector[(T_1 * v_2)]) → d_2
  68. Rotate(k_1, (((T_2 - 1) * 180))°, Q) → s_1
  69. Translate(s_1, Vector[((T_2 - 1) * v_1)]) → c_2
  70. Segment(S, R) → i_1
  71. Segment(Q, R) → j_1
  72. Line(A, D) → m_1
  73. Line(A, B) → n_0
  74. Line(C, D) → n_1
  75. If(x(A) > x(B), y > (Slope[n_0] * (x - x(A))) + y(A), y < (Slope[n_0] * (x - x(A))) + y(A)) → v
  76. If(x(C) > x(D), y > (Slope[n_1] * (x - x(D))) + y(D), y < (Slope[n_1] * (x - x(D))) + y(D)) → w
  77. Line(B, D) → l_1
  78. Line(A, C) → a_2
  79. If(x(C) > x(A), y > (Slope[a_2] * (x - x(A))) + y(A), y < (Slope[a_2] * (x - x(A))) + y(A)) → o_1
  80. ClosestPoint(a_2, B) → F
  81. Line(B, F) → b_2
  82. Circle(F, Ds) → e_2
  83. Intersect(e_2, b_2, 1) → G
  84. ClosestPoint(a_2, D) → H
  85. Line(H, D) → f_2
  86. Circle(H, Ds) → g_2
  87. Intersect(g_2, f_2, 2) → I
  88. ClosestPoint(l_1, C) → J
  89. Line(J, C) → h_2
  90. Circle(J, Ds) → k_2
  91. Intersect(k_2, h_2, 2) → K
  92. ClosestPoint(l_1, A) → L
  93. Line(L, A) → i_2
  94. Circle(L, Ds) → p_2
  95. Intersect(p_2, i_2, 2) → M
  96. ClosestPoint(m_0, D) → N
  97. Line(N, D) → j_2
  98. Circle(N, Ds) → q_2
  99. Intersect(q_2, j_2, 2) → O
  100. ClosestPoint(m_0, A) → T
  101. Circle(T, Ds) → r_2
  102. Line(A, T) → l_2
  103. Intersect(r_2, l_2, 1) → U
  104. ClosestPoint(m_1, B) → V
  105. Line(B, V) → n_2
  106. Circle(V, Ds) → s_2
  107. Intersect(s_2, n_2, 1) → W
  108. ClosestPoint(m_1, C) → Z
  109. Line(Z, C) → t_2
  110. Circle(Z, Ds) → c_3
  111. Intersect(c_3, t_2, 2) → E_1
  112. ClosestPoint(n_0, D) → F_1
  113. Line(F_1, D) → a_3
  114. Circle(F_1, Ds) → d_3
  115. Intersect(d_3, a_3, 2) → G_1
  116. ClosestPoint(n_0, C) → H_1
  117. Line(H_1, C) → b_3
  118. Circle(H_1, Ds) → e_3
  119. Intersect(e_3, b_3, 2) → I_1
  120. ClosestPoint(n_1, B) → J_1
  121. Line(B, J_1) → f_3
  122. Circle(J_1, Ds) → g_3
  123. Intersect(g_3, f_3, 1) → K_1
  124. ClosestPoint(n_1, A) → L_1
  125. Line(A, L_1) → h_3
  126. Circle(L_1, Ds) → k_3
  127. Intersect(k_3, h_3, 1) → M_1
  128. CircleSector(A, A_1, A_2) → r
  129. SelectedIndex(Bahasa) → nn