30°-60°直角三角形边长关系

30°-60°直角三角形边长关系
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2015-09-16 16:45
①本范例演示30°-60°直角三角形三边长度比例关系;②涉及核心概念:特殊三角形性质、三角函数、几何作图;③构造要点:使用Point, Segment, Circle, Midpoint, Intersect, Polygon, Angle, PolyLine等命令绘制并分析三角形及内切圆;④适合初中及以上学生学习特殊三角形性质及几何作图。

GeoGebra 命令及参数

  1. Point(Circle[A, a]) → B_2
  2. Segment(A, B_2) → b
  3. Circle(A, B_2) → c
  4. Circle(B_2, A) → d
  5. Midpoint(b) → B
  6. Intersect(c, d) → C, E, ,
  7. Segment(C, A) → e
  8. Segment(C, B) → f
  9. Segment(C, B_2) → g
  10. Polygon(C, B, A) → poly1, a_1, d_1, c_1
  11. Polygon(C, B_2, B) → poly2, c_2, d_2, b_1
  12. Angle(C, B, A) → α
  13. Angle(B, A, C) → β
  14. Angle(A, C, B) → γ
  15. Midpoint(e) → F
  16. Midpoint(f) → G
  17. Segment(A, B) → h_1
  18. Midpoint(h_1) → H
  19. Midpoint(H, B) → I
  20. Midpoint(I, H) → J
  21. PolyLine(F, J, G) → i
  22. Point(i) → K
  23. Midpoint(F, J) → L
  24. Midpoint(J, G) → M
  25. Intersect(xAxis, yAxis) → O
  26. Point(Circle[O, h]) → P
  27. Segment(O, P) → l
  28. Circle(O, P) → p
  29. Circle(P, O) → q
  30. Intersect(p, q, 1) → Q
  31. Midpoint(l) → R
  32. Segment(O, Q) → m
  33. Segment(R, Q) → n
  34. Segment(O, R) → r
  35. Polygon(O, R, Q) → poly3, q_1, o, r_1
  36. Midpoint(m) → S
  37. Midpoint(l) → T
  38. Midpoint(n) → U
  39. Midpoint(O, R) → A_1
  40. Midpoint(A_1, R) → B_1
  41. Midpoint(B_1, A_1) → C_1
  42. PolyLine(U, C_1, S) → s
  43. Point(s) → D_1
  44. Midpoint(S, C_1) → E_1
  45. Midpoint(C_1, U) → V
  46. Polygon(Q, O, R) → poly4, r_2, q_2, o_1
  47. Angle(R, O, Q) → δ
  48. Angle(O, Q, R) → ε
  49. Angle(Q, R, O) → ζ