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具有相同周长的形状

具有相同周长的形状
几何画板及绘图内容加载中，请稍等……
2018-01-23 23:05
多边形变换几何作图
这个范例展示了具有相同周长的不同形状。它涉及相似变换和几何作图的核心概念。通过使用GeoGebra命令如Line, Intersect, Point, Join等，可以构造出具有相同周长的四边形。适合初中数学教学和学习。

GeoGebra 命令及参数

  1. Line(A, B) → h
  2. Line(D, h) → i
  3. Line(A, D) → f
  4. Line(B, f) → g
  5. Intersect(i, g) → C
  6. Point(GridSpaceQ) → Q
  7. Join(Sequence[Sequence[(i, j), i, 34, 74, 1], j, 12, 32, 1]) → GridSpace
  8. Point(GridSpace) → P
  9. Line(P, Q) → j
  10. Point(GridSpace) → S
  11. Line(S, j) → k
  12. Line(P, S) → l
  13. Line(Q, l) → m
  14. Intersect(m, k) → R
  15. Segment(S, R) → RS
  16. Segment(C, D) → CD
  17. Segment(A, B) → AB
  18. Segment(B, C) → BC
  19. Segment(D, A) → DA
  20. Segment(Q, P) → PQ
  21. Segment(R, Q) → QR
  22. Segment(P, S) → SP
  23. Point(GridSpace) → P2
  24. Point(GridSpace) → Q2
  25. Segment(A2, B2) → AB2
  26. Segment(B2, C2) → BC2
  27. Segment(C2, A2) → CA2
  28. Segment(P2, Q2) → PQ2
  29. Point(GridSpaceR) → R2
  30. Segment(Q2, R2) → QR2
  31. Segment(R2, P2) → RP2
  32. Intersect(OrthogonalLine[A2, Line[B2, C2]], Line[B2, C2]) → H2Tri
  33. Segment(H2Tri, H1Tri) → HeightDisp1Tri
  34. Intersect(OrthogonalLine[P2, Line[Q2, R2]], Line[Q2, R2]) → H4Tri
  35. Segment(H4Tri, H3Tri) → HeightDisp2Tri
  36. Intersect(OrthogonalLine[B, Line[C, D]], Line[C, D]) → H2Quad
  37. Intersect(OrthogonalLine[Q, Line[R, S]], Line[R, S]) → H4Quad
  38. Segment(H2Quad, H1Quad) → HeightDisp1Quad
  39. Segment(H4Quad, H3Quad) → HeightDisp2Quad
  40. Segment(H4Tri, Q2) → HeightDispHoriz2Tri
  41. Segment(H2Tri, B2) → HeightDispHoriz1Tri
  42. Segment(H4Quad, S) → HeightDispHoriz2Quad
  43. Segment(H2Quad, C) → HeightDispHoriz1Quad
  44. Angle(A2, H2Tri, C2) → Ang1Tri
  45. Angle(P2, H4Tri, R2) → Ang2Tri
  46. Angle(B, H2Quad, C) → Ang1Quad
  47. Angle(Q, H4Quad, R) → Ang2Quad
  48. Rotate(A2, 2, B2) → A2'
  49. Angle(C2, B2, A2) → AngABCRtTri
  50. Angle(A, B, C) → AngABCRtQuad
  51. Angle(A2, C2, B2) → AngACBRtTri
  52. Angle(R2, Q2, P2) → AngPQRRtTri
  53. Angle(Q2, R2, P2) → AngPRQRtTri
  54. Angle(P, Q, R) → AngPQRRtQuad