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钝角三角形面积 by sureshbabupp

钝角三角形面积 by sureshbabupp
几何画板及绘图内容加载中，请稍等……
2012-04-05 16:33
测试改名0三角函数几何作图
①本范例演示钝角三角形的面积计算，特别说明其高线可能位于三角形外部；②涉及核心概念包括三角形面积公式、钝角特性、高线定义；③作图要点：使用Point, Segment, Rotate, Angle, OrthogonalLine, Line, Circle, Intersect, Distance, Midpoint, Polygon, Dilate, Vector, Translate等GeoGebra命令构建图形并计算；④适合高中数学教学，用于理解钝角三角形面积计算方法及高线位置特性。

GeoGebra 命令及参数

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → c
  3. Rotate(B, α, A) → B'_1
  4. Angle(B, A, B'_1) → β
  5. OrthogonalLine(A, c) → d
  6. Line(A, B'_1) → g
  7. Line(A, B) → e
  8. Point(e) → C
  9. Circle(C, b) → f
  10. Intersect(f, g) → D, E
  11. Segment(E, B) → h
  12. Distance(E, C) → distanceEC
  13. Distance(A, B) → distanceAB
  14. OrthogonalLine(E, d) → i
  15. OrthogonalLine(B, e) → k
  16. Intersect(i, k) → F
  17. Intersect(i, d) → G
  18. Midpoint(G, F) → H
  19. Midpoint(A, B) → I
  20. Polygon(A, I, H, G) → poly1, a_1, i_1, h_1, g_1
  21. Distance(G, H) → distanceGH
  22. Distance(G, A) → distanceGA
  23. OrthogonalLine(E, e) → l
  24. Intersect(l, e) → J
  25. Distance(J, E) → distanceJE
  26. Midpoint(E, A) → K
  27. Line(K, e) → m
  28. Intersect(m, d) → L
  29. Intersect(h, m) → M
  30. Polygon(A, B, M, L) → poly2, a_2, b_1, m_1, l_1
  31. Polygon(A, L, K) → poly3, k_1, a_3, l_2
  32. Polygon(E, K, M) → poly4, m_2, e_1, k_2
  33. Rotate(M, γ, M) → M'_1
  34. Rotate(E, -γ, M'_1) → E'
  35. Rotate(K, -γ, M'_1) → K'_1
  36. Rotate(M, -γ, M'_1) → M'
  37. Polygon(E', K'_1, M') → poly4', m'_1, e'_1, k'_1
  38. Dilate(B, j, A) → B'
  39. Vector(A, B') → u
  40. Translate(A, u) → A'
  41. Translate(L, u) → L'
  42. Translate(K, u) → K'
  43. Polygon(A', L', K') → poly3', k', a', l'
  44. Distance(A, L) → distanceAL