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三角形特殊线段（动态演示与定理发现）

三角形特殊线段（动态演示与定理发现）
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2016-11-13 08:37
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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
①本范例动态演示了通过三角形某边中点的平行线性质；②涉及核心概念：平行线、三角形中位线定理、动态几何探究；③作图要点：运用了Ray, Segment, Rotate, Angle, Point, Midpoint, Circle, Intersect, Line, Polygon, Vector, Translate等GeoGebra命令与对象；④适合高中数学教学，用于启发学生对几何定理的直观理解与证明探索。

GeoGebra 命令及参数

  1. Ray(A, B) → f
  2. Segment(A, B) → g
  3. Rotate(B, α, A) → B'
  4. Angle(B, A, B') → β
  5. Ray(A, B') → h
  6. Point(h) → C
  7. Segment(C, B) → i
  8. Segment(A, C) → j
  9. Midpoint(j) → D
  10. Midpoint(i) → E
  11. Segment(D, E) → k
  12. Midpoint(k) → F
  13. Min({j / 2, k / 2}) → a
  14. Circle(A, (0.35 * a)) → c
  15. Intersect(c, j, 1) → G
  16. Intersect(c, g, 1) → H
  17. CircleSector(A, H, G) → d
  18. Line(D, E) → l
  19. Circle(D, 2) → e
  20. Circle(E, 2) → p
  21. Intersect(e, l, 1) → I
  22. Intersect(p, l, 2) → J
  23. Ray(D, I) → m
  24. Ray(E, J) → n
  25. Polygon(A, B, C) → poly1, c_1, a_1, b
  26. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  27. Segment(A, A') → q
  28. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_1
  29. Segment(A, A'_1) → r
  30. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], C) → D'
  31. Segment(D, D') → s
  32. Rotate(A, If[3 < o ≤ 4, ((o - 3) * π), π], D) → A'_2
  33. Rotate(A'_1, If[3 < o ≤ 4, ((o - 3) * π), π], D) → K
  34. Segment(A'_2, K) → r'
  35. Dilate(B, If[4 < o ≤ 5, 5 - o, 0], E) → B'_1
  36. Segment(B, B'_1) → t
  37. Dilate(E, If[5 < o ≤ 6, 6 - o, 0], C) → E'
  38. Segment(E, E') → f_1
  39. Rotate(B, If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], E) → B'_2
  40. Rotate(B'_1, If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], E) → L
  41. Segment(B'_2, L) → t'
  42. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], F) → D'_1
  43. Segment(D, D'_1) → g_1
  44. Dilate(A, If[8 < o ≤ 9, 9 - o, 0], D) → A'_3
  45. Vector(A, A'_3) → u
  46. Translate(d, u) → d'
  47. Dilate(F, If[9 < o ≤ 10, 10 - o, 0], E) → F'
  48. Segment(F, F') → h_1