比例测量与尺度探索：通过动态调整图形理解相似与缩放

GeoGebra 命令及参数

1. Vector((0, M_2)) → M_3
2. Vector((M_1, 0)) → M_4
3. Translate(A, M_4) → D
4. Dilate(D, 1 + 1 / ((2 * M_1)), A) → A'
5. Translate(A', M_3) → A''
6. OrthogonalLine(A, b) → c
7. OrthogonalLine(A, c) → d
8. Translate(A, M_3) → B
9. OrthogonalLine(D, c) → e
10. OrthogonalLine(B, d) → f
11. Intersect(e, f) → C
12. Translate(A', M_4) → A''_1
13. Dilate(A''_1, S_1, A') → D'
14. OrthogonalLine(D', c) → g
15. Dilate(A'', If[LockProportions, S_1, S_2], A') → B'
16. OrthogonalLine(B', g) → h
17. Segment(A, D) → i
18. Point(i) → E
19. Vector(A, E) → u
20. Translate(B, u) → B'_1
21. Translate(C, u) → C'_1
22. Translate(B', u) → B''
23. Intersect(g, h) → C'
24. Translate(C', u) → C''
25. Segment(E, B'_1) → j
26. Translate(A', u) → A''_2
27. Dilate(A''_2, S_1, A') → E'
28. Dilate(B'', S_1, B') → B'_2
29. Dilate(C'', S_1, C') → C'_2
30. Polygon(A, B'_1, C'_1, D) → poly1, a_1, b'_1, c'_1, d_1
31. Polygon(A', B'_2, C'_2, D') → poly2, a', b'_2, c'_2, d'
32. Segment(B'_2, E') → k
33. Polygon(A, B'_1, D) → poly3, d_2, a_2, b'_3
34. Polygon(A', B'_2, D') → poly4, d'_1, a'_1, b'_4
35. Midpoint(j) → F
36. Rotate(F, 180*°, E) → F'
37. Polygon(A, F', D, F) → poly5, a_3, f', d_3, f_1
38. Midpoint(k) → G
39. Rotate(G, 180*°, E') → G'
40. Polygon(A', G, D', G') → poly6, a'_2, g_1, d'_2, g'
41. Circle(A, D) → p
42. Segment(A', D') → l
43. PointIn(poly1) → Pointpoly1
44. PointIn(poly2) → Pointpoly2
45. Circle(D', A') → q
46. PointIn(poly3) → Pointpoly3
47. PointIn(poly4) → Pointpoly4
48. Segment(E, F) → m
49. Segment(E, F') → n
50. Segment(E', G) → r
51. Segment(E', G') → s
52. Segment(E, A) → t
53. Segment(E, D) → b_1
54. Segment(A', E') → c_1
55. Segment(E', D') → e_1
56. PointIn(poly5) → Pointpoly5
57. PointIn(poly6) → Pointpoly6
58. Area(p) → o
59. PointIn(p) → Pointp
60. Area(q) → v
61. PointIn(q) → Pointq
62. Intersect(p, d, 1) → H
63. Intersect(q, g, 1) → I
64. Segment(A, (x(A), y(A) + M_2)) → i_1
65. Segment(D', (x(D'), y(D') + (M_2 * If[LockProportions, S_1, S_2]))) → j_1