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Properties of a Regular Hexagon

Properties of a Regular Hexagon
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2018-02-26 18:02
PolygonAngleGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates the properties of a regular hexagon, including side lengths, diagonal lengths, and interior and exterior angles. Key mathematical concepts include polygons, angles, and geometric construction. It uses commands like Polygon, Midpoint, Rotate, CircleArc, and Intersect in GeoGebra for construction. Suitable for students at the middle school level and above to learn about the properties of geometric shapes.

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') → II
  24. Intersect(n, j) → R
  25. Intersect(n, a_1) → S
  26. Segment(R, S) → p
  27. Segment(F, S) → q
  28. Mirror(F, g) → H
  29. Mirror(G, g) → I
  30. Segment(I, E) → r
  31. CircleArc(E, B, H) → t
  32. Polygon(I, E, B) → driehoek3, b_2, i_1, e_4
  33. Rotate(I, (((s - 3) * 180))°, r) → I'
  34. Rotate(E, (((s - 3) * 180))°, r) → E'_1
  35. Rotate(B, (((s - 3) * 180))°, r) → B'
  36. Polygon(I', E'_1, B') → driehoek3', b', i', e'_1
  37. Polygon(E, I, A, C, G) → veelhoek2, e_5, i_2, a_2, c_2, g_4
  38. Segment(B, E) → h_1
  39. Segment(B, I) → j_1
  40. Mirror(R, g) → TT
  41. Mirror(S, g) → SS
  42. Segment(SS, TT) → k_1
  43. Segment(SS, H) → l_1
  44. Polygon(I, H, E) → driehoek4, e_6, i_3, h_2
  45. Circle(G, C) → p_1
  46. Intersect(d', f_1) → J
  47. Intersect(d', f_1) → K
  48. Intersect(d', f_1) → L
  49. Intersect(d', f_1) → M
  50. Intersect(p_1, f_1) → N,
  51. CircleArc(G, N, C) → q_1
  52. Line(G, F) → m_1
  53. Intersect(m_1, a_2) → O
  54. Segment(O, F) → n_1
  55. Polygon(O, C, G) → driehoek5, g_5, o, c_3
  56. Rotate(O, (((s - 5) * 180))°, c_3) → O'
  57. Rotate(C, (((s - 5) * 180))°, c_3) → C'
  58. Rotate(G, (((s - 5) * 180))°, c_3) → G'_1
  59. Polygon(O', C', G'_1) → driehoek5', g'_1, o', c'
  60. Polygon(I, A, O, G, E) → veelhoek3, i_4, a_3, o_1, g_6, e_7
  61. Mirror(O, n_1) → O'_1
  62. Mirror(C, n_1) → C'_1
  63. Mirror(G, n_1) → G'_2
  64. Polygon(O'_1, C'_1, G'_2) → driehoek5'_1, g'_2, o'_1, c'_1
  65. Mirror(O, g) → O'_2
  66. Mirror(C, g) → C'_2
  67. Mirror(G, g) → G'_3
  68. Polygon(O'_2, C'_2, G'_3) → driehoek5'_2, g'_3, o'_2, c'_2
  69. Rotate(O, (((s - 5) * 180))°, c_3) → O'_3
  70. Rotate(G, (((s - 5) * 180))°, c_3) → G'_4
  71. Rotate(O'_2, (((-(s - 6)) * 180))°, c'_2) → Q
  72. Rotate(G'_3, (((-(s - 6)) * 180))°, c'_2) → U
  73. Intersect(c', o_1) → V
  74. Intersect(c', o_1) → W
  75. Intersect(c', o_1) → Z
  76. Line(I, H) → r_1
  77. Intersect(o_1, r_1) → T
  78. Segment(O, C) → s_1
  79. Segment(C, G) → t_1
  80. Polygon(I, A, O, T) → vierhoek2, i_5, a_4, o_2, t_2
  81. Rotate(I, (((-(s - 7)) * 180))°, t_2) → I'_1
  82. Rotate(A, (((-(s - 7)) * 180))°, t_2) → A'
  83. Rotate(O, (((-(s - 7)) * 180))°, t_2) → O'_4
  84. Rotate(T, (((-(s - 7)) * 180))°, t_2) → T'
  85. Polygon(I, T, G, E) → vierhoek3, i_6, t_3, g_7, e_8
  86. Segment(E, T) → f_2
  87. Segment(T, E) → j_2
  88. Intersect(Segment[O, N], j_2) → A_1
  89. Segment(A_1, E) → k_2
  90. Rotate(I, (((-(s - 7)) * 180))°, i_6) → I'_2
  91. Rotate(A, (((-(s - 7)) * 180))°, i_6) → A'_1
  92. Rotate(O, (((-(s - 7)) * 180))°, i_6) → O'_5
  93. Rotate(T, (((-(s - 7)) * 180))°, i_6) → T'_1
  94. Polygon(I'_2, A'_1, O'_5, T'_1) → vierhoek2', i'_2, a'_1, o'_5, t'_1
  95. Mirror(N, g) → NN
  96. CircleArc(I, A, NN) → d_2
  97. Segment(I, T) → l_2
  98. Intersect(g'_2, l_2) → B_1
  99. Polygon(N, B_1, T, G) → vierhoek4, n_2, b_3, t_4, g_8
  100. Segment(I, A) → m_2
  101. Segment(A, O) → p_2
  102. Mirror(H, Segment[I, G]) → HH
  103. Mirror(HH, g) → GG
  104. Intersect(n_2, g) → C_1
  105. Polygon(I, T, C_1, NN) → vierhoek5, i_7, t_5, c_4, nn
  106. Segment(HH, H) → q_2
  107. Segment(GG, F) → r_2
  108. Polygon(GG, F, G) → driehoek6, g_9, gg, f_3
  109. Polygon(I, H, HH) → driehoek7, hh, i_8, h_3
  110. Rotate(GG, (((s - 9) * 180))°, q) → GG'
  111. Rotate(F, (((s - 9) * 180))°, q) → F'
  112. Rotate(G, (((s - 9) * 180))°, q) → G'_5
  113. Polygon(GG', F', G'_5) → driehoek6', g'_5, gg', f'
  114. Rotate(I, (((s - 9) * 180))°, f) → I'_3
  115. Rotate(H, (((s - 9) * 180))°, f) → H'
  116. Rotate(HH, (((s - 9) * 180))°, f) → HH'
  117. Polygon(I'_3, H', HH') → driehoek7', hh', i'_3, h'
  118. Segment(HH, E) → s_2
  119. Segment(H, B_1) → j_3
  120. Segment(E, GG) → k_3
  121. Segment(T, F) → l_3
  122. Polygon(E, HH, H, T, F, GG) → veelhoek4, e_9, hh_1, h_4, t_6, f_4, gg_1
  123. Segment(C_1, T) → m_3
  124. Angle(HH, E, GG) → α
  125. Angle(HH, E, GG) → β
  126. Angle(H', HH, E) → γ
  127. Angle(T, H', HH) → δ
  128. Angle(F, T, H') → ε
  129. Angle(GG, F, T) → ζ
  130. Angle(E, GG, F) → η
  131. Midpoint(E, T) → MM
  132. Circle(MM, E) → d_3
  133. Point(d_3) → PP
  134. Mirror(PP, MM) → PP'
  135. Line(PP, PP') → n_3
  136. Circle(MM, 0.55) → p_3
  137. Line(E, T) → q_3
  138. Intersect(p_3, q_3) → F_1, G_1
  139. Segment(F_1, G_1) → r_3
  140. Sequence(Segment[Rotate[F_1, ((nnn * 30))°, MM], Rotate[G_1, ((nnn * 30))°, MM]], nnn, 1, 6) → lijst_1

AI Drawing Prompt Reference

Draw a regular hexagon with its sides, diagonals, interior angles, and exterior angles. Start by plotting the vertices A, C, D, and B, then connect them to form the hexagon. Construct the diagonals and center point E, and use rotation and symmetry to build the rest of the hexagon, forming multiple triangles and quadrilaterals to demonstrate the symmetry and angle properties of the regular hexagon.
The prompt above was compiled from the original drawing commands and is for reference only.