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多边形全等性探究

多边形全等性探究
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2018-01-20 00:39
多边形几何作图
①本范例演示如何通过变换判断多边形是否全等；②涉及核心概念：全等性、平移、旋转、随机数生成；③构造要点：使用Polygon、Translate、Random命令创建多边形并进行变换；④适合初中及以上学生，用于理解几何变换与多边形性质。

GeoGebra 命令及参数

  1. Polygon((1.5, 2), (3.5, 2), (4, 3), (3, 5), (1, 4)) → Pent1, m, n, p, q, r
  2. Polygon((1, 2), (4, 2), (2, 5)) → Triangle1, f, g, h
  3. Polygon((1, 2), (4, 2), (4, 5), (2, 4)) → Quad1, i, j, k, l
  4. Polygon((7.3, 5.8), (9.8, 5.8), (9.8, 6.5), (7.3, 6.5)) → Box1, s, t, b, c
  5. Translate(Rotate[Translate[Rotate[Pent1, RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Pent2
  6. Polygon((10, 5.8), (12.5, 5.8), (12.5, 6.5), (10, 6.5)) → Box2, d, e, f_1, g_1
  7. Translate(Rotate[Translate[Rotate[Triangle1, RotAngle, RotPt], (8, 0)], a, RotPt2], (move, 0)) → Triangle2
  8. Translate(Rotate[Translate[Rotate[Quad1, RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Quad2
  9. Random(1, 3) → ans
  10. Translate(Rotate[Translate[Rotate[Polygon[(2, 2), (4, 2), (2, 5)], RotAngle, RotPt], (8, 0)], a, RotPt2], (move, 0)) → Triangle2Wrong1
  11. Translate(Rotate[Translate[Rotate[Dilate[Triangle1, 0.7, RotPt], RotAngle, RotPt], (8, 0)], a, RotPt2], (move, 0)) → Triangle2Wrong2
  12. Translate(Rotate[Translate[Rotate[Polygon[(1, 2), (4, 2), (4, 4), (2, 4)], RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Quad2Wrong1
  13. Translate(Rotate[Translate[Rotate[Dilate[Quad1, 0.7, RotPt], RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Quad2Wrong2
  14. Translate(Rotate[Translate[Rotate[Polygon[(1.5, 2), (3.5, 2), (4, 3), (3, 5), (1, 3)], RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Pent2Wrong1
  15. Translate(Rotate[Translate[Rotate[Dilate[Pent1, 0.7, RotPt], RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Pent2Wrong2
  16. Translate(RotPt2 + (-0.3, 0.4), (move, 0)) → LabBPt