任意四边形的中点构成平行四边形

GeoGebra 命令及参数

1. Polygon(A, B, C, D) → poly1, a, b, c, d
2. Midpoint(A, B) → E
3. Midpoint(B, C) → F
4. Midpoint(C, D) → G
5. Midpoint(D, A) → H
6. Polygon(E, F, G, H) → poly2, e, f, g, h
7. Dilate(A, If[0 < i ≤ 1, 1 - i, 0], E) → A'
8. Dilate(B, If[0 < i ≤ 1, 1 - i, 0], F) → B'
9. Dilate(C, If[0 < i ≤ 1, 1 - i, 0], G) → C'
10. Dilate(D, If[0 < i ≤ 1, 1 - i, 0], H) → D'
11. Segment(A, A') → j
12. Segment(B, B') → k
13. Segment(C, C') → l
14. Segment(D, D') → m
15. Dilate(E, If[1 < i ≤ 2, 2 - i, 0], B) → E'
16. Dilate(F, If[1 < i ≤ 2, 2 - i, 0], C) → F'
17. Dilate(G, If[1 < i ≤ 2, 2 - i, 0], D) → G'
18. Dilate(H, If[1 < i ≤ 2, 2 - i, 0], A) → H'
19. Segment(E, E') → n
20. Segment(F, F') → p
21. Segment(G, G') → q
22. Segment(H, H') → r
23. Rotate(A, If[2 < i ≤ 3, ((-(i - 2)) * π), (-π)], E) → A'_1
24. Rotate(A', If[2 < i ≤ 3, ((-(i - 2)) * π), (-π)], E) → A''
25. Segment(A'_1, A'') → j'
26. Rotate(B, If[2 < i ≤ 3, ((-(i - 2)) * π), (-π)], F) → B'_1
27. Rotate(B', If[2 < i ≤ 3, ((-(i - 2)) * π), (-π)], F) → B''
28. Segment(B'_1, B'') → k'
29. Rotate(C, If[2 < i ≤ 3, ((-(i - 2)) * π), (-π)], G) → C'_1
30. Rotate(C', If[2 < i ≤ 3, ((-(i - 2)) * π), (-π)], G) → C''
31. Segment(C'_1, C'') → l'
32. Rotate(D, If[2 < i ≤ 3, ((-(i - 2)) * π), (-π)], H) → D'_1
33. Rotate(D', If[2 < i ≤ 3, ((-(i - 2)) * π), (-π)], H) → D''
34. Segment(D'_1, D'') → m'
35. Dilate(E, If[3 < i ≤ 4, 4 - i, 0], F) → E'_1
36. Segment(E, E'_1) → s
37. Dilate(F, If[4 < i ≤ 5, 5 - i, 0], G) → F'_1
38. Segment(F, F'_1) → t
39. Dilate(E, If[5 < i ≤ 6, 6 - i, 0], H) → E'_2
40. Vector(E, E'_2) → u
41. Translate(E, u) → E'_3
42. Translate(E'_1, u) → I
43. Segment(E'_3, I) → s'
44. Dilate(G, If[6 < i ≤ 7, 7 - i, 0], H) → G'_1
45. Vector(G, G'_1) → v
46. Translate(F, v) → F'_2
47. Translate(F'_1, v) → J
48. Segment(F'_2, J) → t'
49. Polygon(E, F, G, H) → poly3, e_1, f_1, g_1, h_1