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30-60-90特殊直角三角形探索学习资源

30-60-90特殊直角三角形探索学习资源
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2016-04-27 20:28
测试改名0圆几何作图
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 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Triangle Theorems Special Right Triangles Special Right Triangles
①本范例演示30-60-90特殊直角三角形的性质与构造；②涉及核心数学概念包括直角三角形、特殊角、边长比例、相似性；③作图要点：运用Polygon（多边形）、Dilate（缩放）、Segment（线段）、Circle（圆）、Intersect（交点）、CircleSector（扇形）、Rotate（旋转）、Vector（向量）、Translate（平移）、Midpoint（中点）、Ray（射线）等GeoGebra命令；④适合高中数学学生用于理解特殊直角三角形的几何性质和探索其应用。

GeoGebra 命令及参数

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], B) → A'
  3. Segment(A, A') → e
  4. Dilate(B, If[1 < d ≤ 2, 2 - d, 0], C) → B'
  5. Dilate(C, If[2 < d ≤ 3, 3 - d, 0], A) → C'
  6. Segment(A, B) → h
  7. Segment(A, C) → i
  8. Segment(B, C) → j
  9. Circle(A, (0.15 * h)) → k
  10. Intersect(k, i, 1) → D
  11. Intersect(k, h, 1) → E
  12. CircleSector(A, E, D) → p
  13. Rotate(A, If[3.5 < d ≤ 4.5, ((d - 3.5) * π / 3), 1.0471975511965976], A) → A'_1
  14. Rotate(A', If[3.5 < d ≤ 4.5, ((d - 3.5) * π / 3), 1.0471975511965976], A) → A''
  15. Segment(A'_1, A'') → e'
  16. Rotate(A, If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * π / 3), -1.0471975511965976], B) → A'_2
  17. Rotate(A', If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * π / 3), -1.0471975511965976], B) → A''_1
  18. Segment(A'_2, A''_1) → e'_1
  19. Dilate(A, If[6 < d ≤ 7, 7 - d, 0], B) → A'_3
  20. Vector(A, A'_3) → u
  21. Translate(p, u) → p'
  22. Rotate(p', If[7 < d ≤ 8, (((d - 7) * 2) * π / 3), 2.0943951023931953], B) → p''
  23. Circle(B, (0.15 * h)) → r
  24. Intersect(r, j, 1) → F
  25. Intersect(r, h, 1) → K
  26. Dilate(B, If[8 < d ≤ 9, 9 - d, 0], C) → B'_1
  27. Vector(B, B'_1) → v
  28. Translate(p'', v) → p'''
  29. Rotate(p''', If[9 < d ≤ 10, (((d - 9) * 2) * π / 3), 2.0943951023931953], C) → t
  30. Circle(C, (0.15 * h)) → c_1
  31. Intersect(c_1, i) → M,
  32. Intersect(c_1, j) → N,
  33. Midpoint(h) → O
  34. Dilate(C, If[10 < d ≤ 11, 11 - d, 0], O) → C'_1
  35. Segment(C, C'_1) → l
  36. Circle(O, (0.15 * h)) → d_1
  37. Segment(C, O) → m
  38. Intersect(d_1, m, 1) → P
  39. Intersect(d_1, h) → Q, R
  40. Polygon(A, O, C) → poly2, c_2, a_1, o
  41. Intersect(c_1, m) → S,
  42. CircleSector(C, S, N) → e_1
  43. CircleSector(O, R, P) → f_1
  44. Segment(O, B) → n
  45. Rotate(e_1, If[13 < d ≤ 14, ((-(d - 13)) * π / 6), -0.5236], C) → h_1
  46. Rotate(O, If[13.25 < d ≤ 14.25, ((-(d - 13.25)) * π), -3.141592653589793], O) → O'
  47. Rotate(B, If[14 < d ≤ 15, ((d - 14) * π), 3.14159], O) → B'_2
  48. Segment(O', B'_2) → n'
  49. Segment(O, B) → b_1
  50. Dilate(C, If[15 < d ≤ 16, 16 - d, 0], A) → C'_2
  51. Vector(C, C'_2) → w
  52. Translate(h_1, w) → q_1
  53. Dilate(C, If[17 < d ≤ 18, 18 - d, 0], A) → C'_3
  54. Vector(C, C'_3) → u_1
  55. Translate(h_1, u_1) → s_1
  56. Rotate(O', If[19 < d ≤ 20, ((d - 19) * π / 3), 1.0472], A) → O''
  57. Rotate(B'_2, If[18.25 < d ≤ 19.25, ((d - 18.25) * π / 3), 1.0471975511965976], A) → U
  58. Segment(O'', U) → n''
  59. Rotate(O'', If[19.25 < d ≤ 20.25, ((d - 19.25) * π), π], O'') → O'''
  60. Rotate(U, If[20 < d ≤ 21, ((d - 20) * π), π], O'') → U'
  61. Segment(O''', U') → n'''
  62. Rotate(f_1, If[12 < d ≤ 13, ((d - 12) * π / 2), 1.5708], O) → g_1
  63. Rotate(q_1, If[16 < d ≤ 17, (((-(d - 16)) * 4) * π / 3), -4.18879], A) → r_1
  64. Rotate(s_1, If[18 < d ≤ 19, (((-(d - 18)) * 7) * π / 6), -3.66519], A) → t_1
  65. Rotate(E, π / 6, A) → E'
  66. Ray(A, E') → f
  67. Circle(A, (0.2 * h)) → q
  68. Intersect(q, f, 1) → G
  69. Segment(A, G) → g

AI 绘图提示语参考

画一个30-60-90特殊直角三角形，展示其边长比例和角度关系。首先绘制一个等边三角形，然后将其一边缩短并缩放，得到一个直角三角形。接着，以直角顶点为圆心画圆，交于斜边和直角边，得到30°和60°角的顶点。再利用旋转和缩放，构造出其他相关图形，如圆扇形和相似三角形，最终呈现一个包含多个几何元素和标注的完整图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。