菱形面积公式的几何构造与动画演示

GeoGebra 命令及参数

1. Segment(A, B) → a
2. Rotate(B, α, A) → D
3. Angle(B, A, D) → β
4. Circle(D, A) → c
5. Circle(B, A) → d
6. Intersect(c, d, 2) → C
7. Segment(B, C) → g
8. Segment(C, D) → h
9. Segment(D, A) → i
10. Segment(A, C) → j
11. Segment(B, D) → k
12. Intersect(j, k) → I
13. OrthogonalLine(I, i) → l
14. OrthogonalLine(I, h) → m
15. Intersect(l, i) → E
16. Intersect(m, h) → F
17. Intersect(l, g) → G
18. Intersect(m, a) → H
19. Circle(I, H) → e
20. Point(e) → T
21. Tangent(T, e) → t,
22. OrthogonalLine(A, t) → p
23. OrthogonalLine(B, t) → q
24. OrthogonalLine(C, t) → r
25. OrthogonalLine(D, t) → s
26. Segment(I, T) → t_1
27. Angle(t_1, m) → γ
28. Intersect(t, p) → J
29. Intersect(t, q) → K
30. Intersect(t, r) → L
31. Intersect(t, s) → M
32. Segment(A, J) → n_1
33. Segment(B, K) → n_2
34. Segment(C, L) → n_3
35. Segment(D, M) → n_4
36. If(0° ≤ γ ≤ 180° - β, (-n_1) + n_2 + n_3 + n_4, 180° - β ≤ γ ≤ 180°, n_1 + n_2 + n_3 - n_4, 180° ≤ γ ≤ 360° - β, n_1 + n_2 - n_3 + n_4, 360° - β ≤ γ ≤ 360°, n_1 - n_2 + n_3 + n_4) → b
37. Polygon(A, B, C, D) → q1, a_1, b_1, c_1, d_1