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垂直于两边的线段关系

垂直于两边的线段关系
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2017-06-26 09:11
多边形向量几何作图
该范例演示了当从四边形的一边作垂线至其相邻两边时，形成的线段之间的关系。核心数学概念包括四边形、垂直线段和相似三角形。使用了旋转、射线、圆、交点、线段、垂直线、角度、放大、多边形、圆扇形、点、中点、向量和平移等GeoGebra命令。适合初中及以上学生学习几何作图和相似三角形的相关知识。

GeoGebra 命令及参数

  1. Rotate(B, (a * π / 180), A) → B'
  2. Ray(A, B') → j
  3. Circle(A, B) → c
  4. Intersect(c, j) → E,
  5. Line(B, E) → m
  6. Segment(A, B) → f
  7. Circle(B, f) → h
  8. Circle(E, f) → d
  9. Intersect(d, h, 1) → C
  10. Line(A, C) → l
  11. Intersect(l, m) → D
  12. Segment(E, C) → i
  13. OrthogonalLine(D, i) → n
  14. Circle(B, f) → e
  15. Angle(B, A, B') → α
  16. Segment(A, E) → g
  17. Segment(B, C) → k
  18. Intersect(n, f) → G
  19. Angle(D, G, A) → β
  20. OrthogonalLine(D, k) → q
  21. OrthogonalLine(D, g) → s
  22. Segment(D, A) → b
  23. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], B) → A'
  24. Segment(A, A') → j_1
  25. Rotate(A, If[1 < u ≤ 2, ((u - 1) * α), α], A) → A'_1
  26. Rotate(A', If[1 < u ≤ 2, ((u - 1) * α), α], A) → A''
  27. Segment(A'_1, A'') → k_1
  28. Rotate(A'_1, If[2 < u ≤ 3, ((u - 2) * (π - α)), π - α], A) → Q
  29. Rotate(A'_1, If[2 < u ≤ 3, ((u - 2) * (π - α)), π - α], E) → R
  30. Rotate(A'', If[2 < u ≤ 3, ((u - 2) * (π - α)), π - α], E) → A'''_1
  31. Segment(R, A'''_1) → m_1
  32. Rotate(R, If[3 < u ≤ 4, ((u - 3) * α), α], C) → R'
  33. Rotate(A'''_1, If[3 < u ≤ 4, ((u - 3) * α), α], C) → S
  34. Segment(R', S) → l_1
  35. Polygon(A, B, C, E) → poly1, r_1, s_1, t_1, a_1
  36. Segment(E, D) → p_1
  37. Circle(A, (0.15 * f)) → d_1
  38. Segment(A, A'') → q_1
  39. Intersect(d_1, q_1) → T,
  40. Intersect(d_1, f) → U,
  41. CircleSector(A, U, T) → e_1
  42. Dilate(A, If[4 < u ≤ 5, 5 - u, 0], D) → A'_2
  43. Dilate(E, If[4 < u ≤ 5, 5 - u, 0], D) → E'
  44. Segment(A, A'_2) → b_1
  45. Segment(A'', E') → f_2
  46. Dilate(D, If[5 < u ≤ 6, 6 - u, 0], B) → D'
  47. Dilate(D, If[5 < u ≤ 6, 6 - u, 0], C) → D'_1
  48. Segment(D, D') → g_2
  49. Segment(D, D'_1) → h_2
  50. Dilate(D, If[6 < u ≤ 7, 7 - u, 0], G) → D'_2
  51. Segment(A, A'') → r_2
  52. Segment(A'', A) → b_2
  53. Segment(A, B) → f_3
  54. Segment(D, G) → g_3
  55. Segment(R, B) → h_3
  56. OrthogonalLine(D, l_1) → i_3
  57. OrthogonalLine(B, b_2) → j_3
  58. Intersect(b_2, j_3) → A_1
  59. Intersect(i_3, b_2) → B_1
  60. Segment(A_1, B_1) → l_3
  61. Point(l_3) → C_1
  62. OrthogonalLine(C_1, l_1) → p
  63. Intersect(p, l_1) → F
  64. Line(A, R) → r
  65. Line(B, A'') → t
  66. Intersect(p, r) → H
  67. Intersect(p, g_3) → I
  68. Intersect(t, p) → J
  69. Midpoint(H, C_1) → K
  70. Midpoint(J, F) → L
  71. Segment(C_1, K) → f_1
  72. Circle(I, f_1) → c_1
  73. Line(D, G) → g_1
  74. Intersect(c_1, g_1) → M, N
  75. Dilate(D, If[6 < u ≤ 7, 7 - u, 0], I) → D'_3
  76. Dilate(I, If[7 < u ≤ 8, 8 - u, 0], N) → I'
  77. Dilate(N, If[8 < u ≤ 9, 9 - u, 0], G) → N'
  78. Segment(D, D'_3) → h_1
  79. Segment(I, I') → i_1
  80. Segment(N, N') → n_1
  81. Dilate(C_1, If[9 < u ≤ 10, 10 - u, 0], K) → O
  82. Segment(C_1, O) → i_2
  83. Dilate(K, If[10 < u ≤ 11, 11 - u, 0], H) → K'
  84. Segment(K, K') → j_2
  85. Dilate(K, If[11 < u ≤ 12, 12 - u, 0], I) → K'_1
  86. Dilate(H, If[11 < u ≤ 12, 12 - u, 0], I) → H'
  87. Segment(H, H') → k_2
  88. Dilate(I, If[12 < u ≤ 13, 13 - u, 0], J) → I'_1
  89. Segment(I, I'_1) → l_2
  90. Dilate(J, If[13 < u ≤ 14, 14 - u, 0], L) → J'
  91. Segment(J, J') → m_2
  92. Dilate(L, If[14 < u ≤ 15, 15 - u, 0], F) → L'
  93. Segment(L, L') → n_2
  94. Angle(R, F, C_1) → γ
  95. Rotate(C_1, If[15 < u ≤ 16, ((-(u - 15)) * π), (-π)], K) → P
  96. Rotate(O, If[15 < u ≤ 16, ((-(u - 15)) * π), (-π)], K) → O'
  97. Segment(P, O') → p_2
  98. Rotate(J, If[16 < u ≤ 17, ((-(u - 16)) * π), (-π)], L) → J'_1
  99. Rotate(J', If[16 < u ≤ 17, ((-(u - 16)) * π), (-π)], L) → J''
  100. Segment(J'_1, J'') → q_2
  101. Dilate(J, If[17 < u ≤ 18, 18 - u, 0], G) → J'_2
  102. Vector(J, J'_2) → v
  103. Translate(J, v) → J'_3
  104. Translate(J', v) → J''_1
  105. Segment(J'_3, J''_1) → s_2
  106. Line(G, l_2) → t_2
  107. Point(t_2) → V
  108. Angle(V, G, D) → δ
  109. Rotate(J'_3, If[18 < u ≤ 19, ((u - 18) * δ), δ], G) → W
  110. Rotate(J''_1, If[18 < u ≤ 19, ((u - 18) * δ), δ], G) → Z
  111. Segment(W, Z) → a_2
  112. Line(H, N) → c_2
  113. Dilate(H, If[19 < u ≤ 20, 20 - u, 0], N) → H'_1
  114. Vector(H, H'_1) → w
  115. Translate(P, w) → P'
  116. Translate(O', w) → O''
  117. Segment(P', O'') → d_2
  118. Rotate(P', If[20 < u ≤ 21, ((-(u - 20)) * (π - δ)), δ - π], N) → P''
  119. Rotate(O'', If[20 < u ≤ 21, ((-(u - 20)) * (π - δ)), δ - π], N) → O'''
  120. Segment(P'', O''') → e_2