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矩形性质探索

矩形性质探索
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2019-10-18 03:09
多边形角解析几何
①本范例演示矩形的几何性质与相关计算；②涉及核心概念：面积、坐标几何、内切圆、角度、中点、对称变换；③作图要点：使用Segment、OrthogonalLine、Point、Intersect、Angle、Midpoint、Polygon、Line、Mirror等命令构建矩形及辅助元素；④适合初中及以上学生学习几何作图与性质探究。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → D
  5. OrthogonalLine(D, b) → d
  6. Intersect(c, d) → C
  7. Segment(D, A) → e
  8. Segment(D, C) → f
  9. Segment(C, B) → g
  10. Angle(C, B, A) → α
  11. Angle(B, A, D) → β
  12. Angle(A, D, C) → γ
  13. Angle(D, C, B) → δ
  14. Midpoint(D, B) → M
  15. Segment(D, M) → h
  16. Segment(M, B) → i
  17. Segment(A, M) → j
  18. Segment(M, C) → k
  19. Angle(B, A, M) → ε
  20. Angle(M, B, A) → ζ
  21. Angle(D, C, M) → η
  22. Angle(M, D, C) → θ
  23. Angle(A, D, M) → ι
  24. Angle(M, A, D) → κ
  25. Angle(C, B, M) → λ
  26. Angle(M, C, B) → μ
  27. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  28. Line(A, C) → n
  29. Mirror(A, n) → A'
  30. Mirror(B, n) → B'
  31. Mirror(C, n) → C'
  32. Polygon(A', B', C') → poly_2, c', a', b'
  33. Polygon(D, A, B) → poly2, b_2, d_1, a_2
  34. Mirror(D, a_2) → D'
  35. Mirror(A, a_2) → A'_1
  36. Mirror(B, a_2) → B'_1
  37. Polygon(D', A'_1, B'_1) → poly2', b'_1, d', a'_1
  38. Polygon(A, B, C, D) → poly3, a_3, b_3, c_2, d_2
  39. Segment(A, C) → q
  40. Segment(D, B) → t