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等腰梯形模板（探究式学习）

等腰梯形模板（探究式学习）
几何画板及绘图内容加载中，请稍等……
2016-10-12 02:54
多边形变换几何作图
所属专题 Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Unit 7: Polygons and Quadrilaterals Quadrilaterals
这个范例演示了等腰梯形的构造过程。核心数学概念包括几何变换、相似变换和多边形。通过使用GeoGebra命令如线、射线、点、中点、斜率、镜像、相似变换、线段、圆、交点、向量、平移、角度、旋转、多边形等，学生可以探究等腰梯形的性质。适合初中和高中学生进行几何探究和学习。

GeoGebra 命令及参数

  1. Line(A, B_1) → a
  2. Ray(A, B_1) → b
  3. Point(b) → B
  4. Midpoint(A, B) → D_1
  5. Line(A, B) → c
  6. Slope(c) → d
  7. OrthogonalLine(D_1, c) → g
  8. Point(g) → E_1
  9. Ray(D_1, E_1) → h
  10. Point(h) → F
  11. Slope(h) → i
  12. Line(F, c) → l
  13. Point(l) → G
  14. Point(l) → H
  15. Ray(F, G) → m
  16. Ray(F, H) → n
  17. Point(m) → D
  18. Mirror(D, h) → I'
  19. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  20. Segment(A, A') → p
  21. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_1
  22. Segment(A, A'_1) → q
  23. Segment(A, B) → r
  24. Segment(B, I') → s
  25. Segment(I', D) → t
  26. Segment(D, A) → a_1
  27. Circle(A, (0.2 * Min[a_1, r])) → c_1
  28. Circle(D, (0.2 * Min[a_1, r])) → d_1
  29. Intersect(d_1, a_1, 1) → J
  30. Intersect(d_1, t, 1) → K
  31. Intersect(c_1, r, 1) → L
  32. Intersect(c_1, a_1, 1) → M
  33. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], I') → I'_1
  34. Segment(D, I'_1) → b_1
  35. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], B) → A'_2
  36. Vector(A, A'_2) → u
  37. Translate(A, u) → A'_3
  38. Translate(A'_1, u) → N
  39. Segment(A'_3, N) → q'
  40. OrthogonalLine(A, r) → g_1
  41. Point(g_1) → O
  42. Angle(D, A, O) → α
  43. Angle(I', B, A) → β
  44. Rotate(A'_3, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → P
  45. Rotate(N, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → C
  46. Segment(P, C) → q''
  47. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], B) → A'_4
  48. Vector(A, A'_4) → v
  49. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
  50. Vector(D, I'_2) → w
  51. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], I') → A'_5
  52. Segment(A, A'_5) → i_1
  53. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], D) → A'_6
  54. Vector(A, A'_6) → u_1
  55. Translate(A, u_1) → A'_7
  56. Translate(A'_5, u_1) → Q
  57. Segment(A'_7, Q) → j_1
  58. Segment(D, B) → l_1
  59. Angle(L, A, I') → γ
  60. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → R
  61. Rotate(Q, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → Q'
  62. Segment(R, Q') → m_1
  63. Polygon(A, B, I', D) → poly1, a_2, c_2, i', i_2
  64. Intersect(i_1, m_1) → E
  65. Distance(A, E) → distanceAS
  66. Distance(E, C) → distanceSN'
  67. Distance(E, B) → distanceSC
  68. Distance(E, D) → distanceSI
  69. Angle(B, A, E) → δ
  70. Angle(E, B, A) → ε
  71. Angle(C, B, E) → ζ
  72. Angle(E, A, D) → η
  73. Angle(A, D, E) → θ
  74. Angle(E, D, C) → ι
  75. Angle(D, C, E) → κ
  76. Angle(B, E, C) → λ
  77. Angle(E, C, B) → μ
  78. Angle(A, E, B) → ν
  79. Polygon(A, B, C) → poly2, c_3, a_3, b_2
  80. Segment(A, C) → h_1
  81. Mirror(A, h_1) → A'_8
  82. Mirror(B, h_1) → B'
  83. Mirror(C, h_1) → C'
  84. Polygon(A'_8, B', C') → poly2', c', a'_8, b'
  85. Polygon(D, A, B) → poly3, b_3, d_2, a_4
  86. Segment(D, B) → p_1
  87. Mirror(D, p_1) → D'
  88. Mirror(A, p_1) → A'_9
  89. Mirror(B, p_1) → B'_1
  90. Polygon(D', A'_9, B'_1) → poly3', b'_1, d', a'_9