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等腰与等边三角形-对称轴

等腰与等边三角形-对称轴
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2016-07-28 22:51
测试改名0几何作图
①本范例演示等腰与等边三角形的对称轴性质；②涉及核心数学概念包括对称性、等腰三角形、等边三角形、中线、角平分线、镜像变换；③作图要点运用了中点(Midpoint)、多边形(Polygon)、线(Line)、线段(Segment)、角平分线(LineBisector)、交点(Intersect)、镜像(Mirror)、距离(Distance)等GeoGebra命令；④适合初中及以上学生学习几何对称性与变换，可用于教学演示或几何作图练习。

GeoGebra 命令及参数

  1. Midpoint(A, C) → P
  2. Midpoint(C, B) → O
  3. Polygon(C, B, A, D) → poly1, a_1, b_1, d_1, c_1
  4. Line(A, B) → j
  5. Line(D, A) → k
  6. Line(C, B) → l
  7. Line(D, C) → m
  8. LineBisector(M, A) → c
  9. Intersect(c, k) → F_1
  10. Intersect(c, l) → G
  11. Intersect(c, m) → H
  12. Intersect(j, c) → I
  13. Mirror(B, c) → B'
  14. Mirror(D, c) → D'
  15. Mirror(C, c) → A'
  16. Polygon(M, F_1, I) → poly2, i, e, f
  17. Polygon(F_1, D, C, B, I) → poly3, f_1, d, a_2, b_2, i_1
  18. Polygon(F_1, M, B', G) → poly4, f_2, e_1, b', g
  19. Polygon(F_1, D, C, G) → poly5, f_3, d_2, a_3, g_1
  20. Polygon(F_1, M, B', A', H) → poly6, f_4, e_2, b'_1, a', h
  21. Polygon(F_1, D, H) → poly7, h_1, f_5, d_3
  22. Polygon(H, D', M, I) → poly8, h_2, d', e_3, i_2
  23. Polygon(H, C, B, I) → poly9, h_3, a_4, b_3, i_3
  24. Polygon(H, D', M, B', G) → poly10, h_4, d'_1, e_4, b'_2, g_2
  25. Polygon(H, C, G) → poly11, g_3, h_5, a_5
  26. Polygon(G, B, I) → poly13, i_4, g_4, b_4
  27. Polygon(G, A', D', M, I) → poly12, n, p, q, r, s
  28. Midpoint(D, A) → E
  29. Midpoint(C, B) → F
  30. Segment(E, F) → t
  31. If(Distance[M, D] ≤ 0.05, 1, 0) → ok
  32. Midpoint(A, M) → J
  33. Midpoint(b_1) → K
  34. Midpoint(c_1) → L
  35. Line(C, K) → a1
  36. Line(D, B) → c1
  37. Segment(A, C) → e1
  38. Segment(C, B) → f1
  39. Distance(C, B) → cc
  40. Distance(C, A) → bb
  41. Distance(A, B) → aa
  42. Segment(A, B) → a
  43. Segment(C, B) → g1
  44. Midpoint(d_1) → N
  45. Line(A, O) → d1
  46. Line(F_1, B) → b
  47. Line(C, I) → h1
  48. Line(A, O) → i1
  49. Polygon(M, C, O) → poly14, o, m_1, a_6
  50. Line(B, P) → j1
  51. Line(P, B) → b1