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Triangle 2 - Dimensions

Triangle 2 - Dimensions
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2018-02-26 17:58
TriangleCoordinate GeometryGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates how to construct an isosceles triangle using GeoGebra and explore its properties. Key mathematical concepts include the properties of isosceles triangles, midpoints, rotations, angle bisectors, and reflections. By using commands like Polygon, Segment, Midpoint, Rotate, and AngularBisector, students can understand the basics of geometric construction. Suitable for middle school and above students to learn about geometric construction and properties of isosceles triangles.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Segment((sqrt(2) / 4, 0), (sqrt(2) / 4, 1)) → f
  3. Segment((sqrt(2) / 2, 0), (sqrt(2) / 2, 1)) → g
  4. Segment(((3 * sqrt(2) / 4), 0), ((3 * sqrt(2) / 4), 1)) → h
  5. Midpoint(B, D) → E
  6. Rotate(D, -90°, E) → DD
  7. CircleArc(E, DD, D) → e
  8. Intersect(e, h, 1) → F
  9. CircleArc(E, F, D) → k
  10. AngularBisector(F, E, D) → i
  11. Intersect(i, c) → G
  12. Segment(E, G) → j
  13. Polygon(A, C, G, E, B) → veelhoek1, a_1, c_1, g_1, e_1, b_1
  14. Polygon(E, D, G) → driehoek1, g_2, e_2, d_1
  15. Rotate(E, (((-(s - 1)) * 180))°, g_1) → E'
  16. Rotate(D, (((-(s - 1)) * 180))°, g_1) → D'
  17. Rotate(G, (((-(s - 1)) * 180))°, g_1) → G'
  18. Polygon(E', D', G') → driehoek1', g', e', d'
  19. Polygon(E, F, G) → driehoek2, g_3, e_3, f_1
  20. Segment(E, D) → l
  21. Segment(D, G) → m
  22. OrthogonalLine(F, a_1) → n
  23. Intersect(j, d') → HH
  24. Intersect(j, d') → II
  25. Intersect(n, j) → R
  26. Intersect(n, a_1) → S
  27. Segment(R, S) → p
  28. Segment(F, S) → q
  29. Mirror(F, g) → H
  30. Mirror(G, g) → I
  31. Segment(I, E) → r
  32. CircleArc(E, B, H) → t
  33. Polygon(I, E, B) → driehoek3, b_2, i_1, e_4
  34. Rotate(I, (((s - 3) * 180))°, r) → I'
  35. Rotate(E, (((s - 3) * 180))°, r) → E'_1
  36. Rotate(B, (((s - 3) * 180))°, r) → B'
  37. Polygon(I', E'_1, B') → driehoek3', b', i', e'_1
  38. Polygon(E, I, A, C, G) → veelhoek2, e_5, i_2, a_2, c_2, g_4
  39. Segment(B, E) → h_1
  40. Segment(B, I) → j_1
  41. Mirror(R, g) → TT
  42. Mirror(S, g) → SS
  43. Segment(SS, TT) → k_1
  44. Segment(SS, H) → l_1
  45. Polygon(I, H, E) → driehoek4, e_6, i_3, h_2
  46. Circle(G, C) → p_1
  47. Intersect(d', f_1) → J
  48. Intersect(d', f_1) → K
  49. Intersect(d', f_1) → L
  50. Intersect(d', f_1) → M
  51. Intersect(p_1, f_1) → N,
  52. CircleArc(G, N, C) → q_1
  53. Line(G, F) → m_1
  54. Intersect(m_1, a_2) → O
  55. Segment(O, F) → n_1
  56. Polygon(O, C, G) → driehoek5, g_5, o, c_3
  57. Rotate(O, (((s - 5) * 180))°, c_3) → O'
  58. Rotate(C, (((s - 5) * 180))°, c_3) → C'
  59. Rotate(G, (((s - 5) * 180))°, c_3) → G'_1
  60. Polygon(O', C', G'_1) → driehoek5', g'_1, o', c'
  61. Polygon(I, A, O, G, E) → veelhoek3, i_4, a_3, o_1, g_6, e_7
  62. Mirror(O, n_1) → O'_1
  63. Mirror(C, n_1) → C'_1
  64. Mirror(G, n_1) → G'_2
  65. Polygon(O'_1, C'_1, G'_2) → driehoek5'_1, g'_2, o'_1, c'_1
  66. Mirror(O, g) → O'_2
  67. Mirror(C, g) → C'_2
  68. Mirror(G, g) → G'_3
  69. Polygon(O'_2, C'_2, G'_3) → driehoek5'_2, g'_3, o'_2, c'_2
  70. Rotate(O, (((s - 5) * 180))°, c_3) → O'_3
  71. Rotate(G, (((s - 5) * 180))°, c_3) → G'_4
  72. Rotate(O'_2, (((-(s - 6)) * 180))°, c'_2) → Q
  73. Rotate(G'_3, (((-(s - 6)) * 180))°, c'_2) → U
  74. Intersect(c', o_1) → V
  75. Intersect(c', o_1) → W
  76. Intersect(c', o_1) → Z
  77. Line(I, H) → r_1
  78. Intersect(o_1, r_1) → T
  79. Segment(O, C) → s_1
  80. Segment(C, G) → t_1
  81. Polygon(I, A, O, T) → vierhoek2, i_5, a_4, o_2, t_2
  82. Rotate(I, (((-(s - 7)) * 180))°, t_2) → I'_1
  83. Rotate(A, (((-(s - 7)) * 180))°, t_2) → A'
  84. Rotate(O, (((-(s - 7)) * 180))°, t_2) → O'_4
  85. Rotate(T, (((-(s - 7)) * 180))°, t_2) → T'
  86. Polygon(I, T, G, E) → vierhoek3, i_6, t_3, g_7, e_8
  87. Segment(E, T) → f_2
  88. Segment(T, E) → j_2
  89. Intersect(Segment[O, N], j_2) → A_1
  90. Segment(A_1, E) → k_2
  91. Rotate(I, (((-(s - 7)) * 180))°, i_6) → I'_2
  92. Rotate(A, (((-(s - 7)) * 180))°, i_6) → A'_1
  93. Rotate(O, (((-(s - 7)) * 180))°, i_6) → O'_5
  94. Rotate(T, (((-(s - 7)) * 180))°, i_6) → T'_1
  95. Polygon(I'_2, A'_1, O'_5, T'_1) → vierhoek2', i'_2, a'_1, o'_5, t'_1
  96. Mirror(N, g) → NN
  97. CircleArc(I, A, NN) → d_2
  98. Segment(I, T) → l_2
  99. Intersect(g'_2, l_2) → B_1
  100. Polygon(N, B_1, T, G) → vierhoek4, n_2, b_3, t_4, g_8
  101. Segment(I, A) → m_2
  102. Segment(A, O) → p_2
  103. Midpoint(B, E) → C_1
  104. Midpoint(I, G) → D_1
  105. Midpoint(E, D) → E_1
  106. Mirror(O, l_2) → OO
  107. Mirror(A, l_2) → AA
  108. Polygon(I, T, OO, AA) → vierhoek5, i_7, t_5, oo, aa
  109. Segment(B_1, OO) → s_2
  110. Intersect(i_3, oo) → F_1
  111. Polygon(F_1, OO, E) → driehoek6, e_9, f_3, oo_1
  112. Polygon(E, T, G) → driehoek7, g_9, e_{10}, t_6
  113. Rotate(E, (((-(s - 9)) * 180))°, g) → E'_2
  114. Rotate(T, (((-(s - 9)) * 180))°, g) → T'_2
  115. Rotate(G, (((-(s - 9)) * 180))°, g) → G'_5
  116. Polygon(E'_2, T'_2, G'_5) → driehoek7', g'_5, e'_2, t'_2
  117. Segment(E, T) → h_3
  118. Segment(OO, E) → j_3
  119. Polygon(I, T, E) → driehoek8, e_{11}, i_8, t_7
  120. OrthogonalLine(I, e_6) → q_2
  121. OrthogonalLine(G, e_3) → r_2
  122. Intersect(r_2, q_2) → G_1
  123. CircleArc(G_1, I, G) → d_3
  124. Angle(E, G, O) → α
  125. Angle(T, I, E) → β
  126. Segment(E, G) → k_3
  127. Segment(T, G) → l_3
  128. Midpoint(I, G) → MM
  129. Angle(MM, E, G) → ε
  130. Segment(MM, G) → m_3
  131. Segment(I, MM) → n_3

AI Drawing Prompt Reference

Draw an isosceles triangle ABC with base BC on the x-axis and vertex A on the y-axis. First, draw the base BC, then find the midpoint E of BC and rotate point D around E to get D'. Next, construct the base and legs of the isosceles triangle using lines and angle bisectors, and reflect to create the altitude and median. Finally, use rotation and reflection to obtain the symmetric image of the isosceles triangle.
The prompt above was compiled from the original drawing commands and is for reference only.