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Properties and Identification of Isosceles Trapezium

Properties and Identification of Isosceles Trapezium
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2023-11-28 20:52
PolygonSequenceCoordinate GeometryTransformationGeometric Construction
In collections Trapez - Eigenschaften und Konstruktionen
This example demonstrates the trapezoid and its properties, including the special properties of isosceles trapezium. It uses multiple-choice and open questions to help students understand the definition, properties, and identification of trapezoids. GeoGebra commands used include Polygon, PointIn, Segment, Point, Angle, Textfield, Sequence, Midpoint, Element, Intersect, Text, If, OrthogonalLine, Rotate. Suitable for 5-6 grade students to learn about the properties and identification of geometric shapes.

GeoGebra Commands & Parameters

  1. Polygon((-3, -1), (6, -1), (6, -3), (-3, -3)) → RegionBox1, j, k, l, m
  2. PointIn(RegionBox1) → A_1
  3. Polygon((x(A_1) + 1.5, 2.02), (8.56, 2.02), (8.56, 0.04), (x(A_1) + 1.5, 0.02)) → RegionBox2, c, d, e, f_1
  4. SelectedIndex(drop5) → index5
  5. SelectedIndex(drop2) → index2
  6. SelectedIndex(drop1) → index1
  7. SelectedIndex(drop3) → index3
  8. SelectedIndex(drop4) → index4
  9. Polygon((-3, 2), (7, 2), (7, 0.02), (-3, 0.02)) → RegionBox, f, g, h, i
  10. PointIn(RegionBox1) → B
  11. Segment(F, B - (0.5, 0)) → bf
  12. PointIn(RegionBox) → D
  13. Segment(D + (0.5, 0), E) → de
  14. Point(de) → C
  15. Segment(D, C) → cd
  16. Point(bf) → A
  17. Segment(D, A) → ad
  18. Segment(A, B) → ab
  19. Segment(C, B) → bc
  20. Angle(B, A, D) → α
  21. Angle(C, B, A) → β
  22. Angle(D, C, B) → γ
  23. Angle(A, D, C) → δ
  24. Textfield(input1) → InputBox1
  25. Textfield(input2) → InputBox2
  26. PointIn(RegionBox2) → C_1
  27. Segment(A_1, B_1) → ab_1
  28. Segment(B_1, C_1) → bc_1
  29. Segment(C_1, D_1) → cd_1
  30. Segment(A_1, D_1) → ad_1
  31. Angle(B_1, A_1, D_1) → ε
  32. Angle(C_1, B_1, A_1) → ζ
  33. Angle(D_1, C_1, B_1) → η
  34. Angle(A_1, D_1, C_1) → θ
  35. Segment(D_1, B_1) → diag1
  36. Segment(A_1, C_1) → diag2
  37. Sequence((0, y(D_1) + 0.5) + (i, 0), i, x(D_1) - 1, x(C_1) + 1, (lengthAB * 0.04)) → points
  38. Sequence((0, y(A_1) - 0.5) + (i, 0), i, x(D_1) - 1, x(C_1) + 1, (lengthAB * 0.04)) → points2
  39. Midpoint(A_1, B_1) → V
  40. Midpoint(D_1, C_1) → G_1
  41. Sequence((x(V) + ((lengthAB * j)) / 10, y(G_1) + 0.5), j, -5, 5) → punkteOben
  42. Point(punkteOben) → Psym1
  43. Sequence((x(V) + ((lengthAB * j)) / 10, y(V) - 0.5), j, -5, 5) → punkteUnten
  44. Point(punkteUnten) → Psym2
  45. Segment(Psym1, Psym2) → sym_{1}
  46. Element(points, sym) → CorrSym
  47. Segment(K, N) → n
  48. Segment(N, M) → p
  49. Segment(M, L) → q
  50. Segment(L, K) → r
  51. Segment(G, J) → s
  52. Segment(J, I) → t
  53. Segment(I, H) → a
  54. Segment(H, G) → b
  55. Segment((Midpoint[D, C] - 0.2, y(D) - 0.2), (Midpoint[D, C] + 0.2, y(D) + 0.2)) → parallel1
  56. Segment(N, L) → g_1
  57. Segment(M, K) → h_1
  58. Intersect(diag1, diag2) → O
  59. Midpoint(O, A_1) → mitte
  60. Text(text21, Midpoint[O, B_1] + v, true, true, 0, 0) → text9
  61. Angle(I, H, G) → ι
  62. Angle(H, G, J) → κ
  63. Angle(J, I, H) → λ
  64. Angle(G, J, I) → μ
  65. Angle(L, K, N) → ν
  66. Angle(N, M, L) → ξ
  67. Angle(M, L, K) → ο
  68. Angle(K, N, M) → ρ
  69. If(x(A) ≠ -0.72 ∨ x(B) ≠ 6 ∨ x(C) ≠ 5.03 ∨ x(D) ≠ 1, true, false) → moved
  70. If(x(A_1) ≠ 0 ∨ x(C_1) ≠ 5 ∨ x(D_1) ≠ 1 ∨ x(B_1) ≠ 6, true, false) → moved2
  71. OrthogonalLine(D, ab) → j_1
  72. Segment(D, P) → k_1
  73. OrthogonalLine(D_1, ab_1) → l_1
  74. Intersect(l_1, ab_1) → Q
  75. Segment(D_1, Q) → m_1
  76. Angle(B_1, Q, D_1) → τ
  77. Text(text20, Midpoint[O, A_1] + u, true, true, 1, 1) → text8
  78. Angle(B + (10, 0), P, D) → σ
  79. Segment(B, P) → n_1
  80. SelectedIndex(drop7) → index7
  81. Point(t) → W
  82. OrthogonalLine(W, b) → p_1
  83. Intersect(p_1, b) → Z
  84. Segment(W, Z) → q_1
  85. Angle(H, Z, W) → υ
  86. Segment(G, I) → r_1
  87. Segment(H, J) → s_1
  88. Point(p) → E_1
  89. OrthogonalLine(E_1, p) → t_1
  90. Intersect(t_1, r) → F_1
  91. Angle(L, F_1, E_1) → ϕ
  92. Segment(E_1, F_1) → a_1
  93. Segment(Midpoint[K, L] + (0, -0.5), Midpoint[M, N] + (0, 0.5)) → i_1
  94. Segment(D + (0, 0.25), D + (0, lengthArrow)) → arrow1
  95. Segment(C_1 + (0, 0.25), C_1 + (0, lengthArrow)) → arrow2
  96. Rotate(arrow2, 270°, C_1) → arrow2'
  97. Rotate(arrow2, 90°, C_1) → arrow2'_{1}
  98. Rotate(arrow2, 180°, C_1) → arrow2'_{2}
  99. Segment(A_1 + (1, -0.13), A_1 + (1, 0.13)) → b_1
  100. Segment(A_1 + (1.1, -0.13), A_1 + (1.1, 0.13)) → c_1
  101. Segment(D_1 + (1, -0.13), D_1 + (1, 0.13)) → d_1
  102. Segment(D_1 + (1.1, -0.13), D_1 + (1.1, 0.13)) → e_1
  103. Segment(Psym1 + (0.25, 0), Psym1 + (lengthArrow, 0)) → f_2
  104. Segment(Psym1 + (-0.25, 0), Psym1 + ((-lengthArrow), 0)) → g_2
  105. Segment(D + (0, 0.25), D + (0, lengthArrow)) → arrow1_{neu}
  106. Rotate(arrow1_{neu}, 270°, D) → arrow1'
  107. Rotate(arrow1_{neu}, 90°, D) → arrow1'_{1}
  108. Rotate(arrow1_{neu}, 180°, D) → arrow1'_{2}
  109. SelectedIndex(drop9) → index9
  110. SelectedIndex(drop6) → index6
  111. Segment(K + (3, -0.15), K + (3, 0.15)) → h_2
  112. Segment(K + (3.1, -0.15), K + (3.1, 0.15)) → i_2
  113. Segment(N + (2.3, -0.15), N + (2.3, 0.15)) → j_2
  114. Segment(N + (2.4, -0.15), N + (2.4, 0.15)) → k_2

AI Drawing Prompt Reference

Draw a trapezoid in the coordinate plane with horizontal bases and vertical sides at x=-3 and x=6: use a region-like trapezoid with top and bottom edges parallel to the x-axis. Choose a point on the first region as A, and choose another point in a second, narrower region to set the opposite pair of vertices, forming a trapezoid with vertices A, B, C, D. Connect the vertices to get its four sides and draw both diagonals AC and BD. Mark four angles around the trapezoid: angle at A between BA and AD, angle at B between AB and BD, angle at C between BC and CA, and angle at D between DC and DA. Compute the midpoint of AB and the midpoint of DC, then use points above and below the midpoint of DC to draw a short segment indicating a symmetry line.
The prompt above was compiled from the original drawing commands and is for reference only.