帕普斯面积定理（二）：一般四边形上的面积关系与几何变换

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. Segment(A, C) → f
3. Segment(A, B) → g
4. Segment(C, B) → h
5. LineBisector(A, B) → i
6. LineBisector(A, C) → j
7. Point(i) → D
8. Point(j) → E
9. Point(j) → F
10. Point(i) → G
11. Line(F, b) → k
12. Line(G, c) → l
13. Mirror(A, G) → A'_{1}
14. Mirror(B, G) → B'
15. Segment(A'_{1}, B') → c'
16. Mirror(C, F) → C'
17. Mirror(A, F) → A'
18. Segment(C', A') → b'
19. Segment(A, B') → m
20. Segment(B, A'_{1}) → n
21. Segment(A, C') → p
22. Segment(C, A') → q
23. Line(A', C') → r
24. Line(B', A'_{1}) → s
25. Intersect(r, s) → H
26. Segment(A, H) → ttt
27. Line(H, A) → d
28. Line(C, d) → e
29. Line(B, d) → f_1
30. Intersect(d, a) → I
31. Midpoint(I, H) → J
32. Mirror(A, J) → A'_{2}
33. Mirror(H, J) → H'
34. Segment(A'_{2}, H') → t'
35. Mirror(A'_{2}, I) → K
36. Mirror(H', I) → H''
37. Segment(K, H'') → tt
38. Line(K, a) → t
39. Intersect(e, t) → L
40. Intersect(f_1, t) → M
41. Intersect(r, t) → N
42. Intersect(s, t) → O
43. Polygon(C, L, K, H'') → q4, c_3, l_2, k_1, h''
44. Polygon(A', C, A, C') → q5, i_1, c_4, a_3, j_1
45. Polygon(H'', K, M, B) → q6, n_1, k_2, m_2, b_3
46. Polygon(A, B, A'_{1}, B') → q7, a_4, b_4, p_1, q_1
47. PointIn(q4) → Pointq4
48. PointIn(q5) → Pointq5
49. PointIn(q6) → Pointq6
50. PointIn(q7) → Pointq7
51. Angle(A, C, B) → α