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构造等面积正方形

构造等面积正方形
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2015-12-16 23:00
多边形解析几何几何作图
本范例演示如何构造一个正方形，使其面积与给定的矩形相等。核心数学概念包括几何作图和面积计算。使用了Segment, OrthogonalLine, Circle, Intersect, Ray, Point, Rotate, Midpoint, Semicircle, Polygon, PointIn等命令。适合初中及以上学生学习几何作图和面积计算。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Circle(A, C) → c
  4. Intersect(c, b) → D, E
  5. Ray(A, E) → d
  6. Point(d) → F
  7. OrthogonalLine(F, d) → e
  8. OrthogonalLine(B, a) → f
  9. Intersect(e, f) → G
  10. Segment(A, F) → g
  11. Segment(F, G) → h
  12. Segment(G, B) → i
  13. Rotate(G, (-(90°)), B) → G'
  14. Segment(B, G') → j
  15. Segment(A, G') → k
  16. Midpoint(k) → H
  17. Semicircle(A, G') → p
  18. OrthogonalLine(B, j) → l
  19. Intersect(p, l, 1) → I
  20. Segment(G, I) → m
  21. Polygon(I, B, 4) → poly1, n, q, r, s, J, K
  22. Polygon(A, F, G, B) → poly2, a_1, f_1, g_1, b_1
  23. PointIn(poly2) → Pointpoly2
  24. PointIn(poly1) → Pointpoly1