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SAS相似定理探索 by Tim Brzezinski

SAS相似定理探索 by Tim Brzezinski
几何画板及绘图内容加载中，请稍等……
2016-03-26 03:11
测试改名0角几何作图滑块动画
所属专题 Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster Similarity Theorems! Similar Triangles Review U9 Dilations and Similar Triangles Similar Triangles Theorem
①本范例演示学生如何通过交互式操作，直观理解并发现三角形的SAS相似定理；②涉及核心数学概念包括三角形相似性、角相等、边比例、几何变换；③作图要点提炼自构造摘要，使用了线段、向量、缩放、多边形、平移、角度、圆、交点、扇形、文本框等GeoGebra命令与对象；④适合高中数学教学，用于帮助学生建立几何直观，深化对相似定理的理解和应用。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(B, C) → b_2
  3. Segment(C, A) → b
  4. Vector(A, D) → u
  5. Dilate(A, k, A) → A'
  6. Dilate(B, k, A) → B'
  7. Segment(A', B') → a'_2
  8. Dilate(C, k, A) → C'
  9. Dilate(A, k, A) → A'_1
  10. Segment(C', A'_1) → c'
  11. Dilate(B, k, A) → B'_1
  12. Dilate(C, k, A) → C'_1
  13. Segment(B'_1, C'_1) → b'_2
  14. Polygon(A'_1, B'_1, C'_1) → poly1, c'_1, a'_1, b'_1
  15. Dilate(A, m, D) → A'_2
  16. Vector(A, A'_2) → v
  17. Translate(A'_1, v) → E
  18. Translate(B'_1, v) → F
  19. Translate(C'_1, v) → G
  20. Polygon(E, F, G) → poly1', g, e, f
  21. Polygon(A, C, B) → poly2, b_1, a_1, c_1
  22. Segment(F, A'_2) → a'
  23. Segment(A'_2, G) → b'
  24. Segment(G, F) → i
  25. Angle(B, A, C) → α
  26. Vector(D, A) → w
  27. Circle(A, 0.5) → p
  28. Intersect(p, a) → H,
  29. Intersect(p, b) → I,
  30. Circle(A'_2, 0.5) → q
  31. Intersect(q, a', 1) → J
  32. Intersect(q, b', 1) → K
  33. CircleSector(A'_2, J, K) → r
  34. CircleSector(A, H, I) → s
  35. Angle(H, A, I) → β
  36. CircleSector(A, I, H) → t
  37. CircleSector(A'_2, K, J) → d_1
  38. Circle(B, 0.5) → c
  39. Circle(F, 0.5) → d
  40. Intersect(c, b_2, 1) → L
  41. Intersect(c, a, 1) → M
  42. Intersect(d, i, 1) → N
  43. Intersect(d, a', 1) → O
  44. CircleSector(F, N, O) → h
  45. CircleSector(B, L, M) → e_1
  46. CircleSector(F, O, N) → f_1
  47. Dilate(F, 1 - j, B) → F'
  48. Vector(F, F') → l
  49. Translate(h, l) → h'
  50. Translate(f_1, l) → g_1
  51. Textfield(k) → InputBox1