梯形面积的倍增构造——动态演示与几何验证

GeoGebra 命令及参数

1. Line(A, xAxis) → a
2. Point(a) → D
3. If(abs(x(H) - x(A)) < 0.2, (x(A), y(H)), H) → Pm
4. DynamicCoordinates(H, x(Pm), y(Pm)) → B
5. Line(B, a) → c
6. Point(c) → C
7. If(p ≟ true, C, D) → Putar
8. Polygon(A, B, C, D) → poly1, a_1, b_1, c_1, d
9. Line(A, yAxis) → b
10. Intersect(c, b) → E
11. If(e ≤ 1, Rotate[B, (180° * e), Putar], Rotate[B, 180°, Putar]) → B'
12. If(e ≤ 1, Rotate[C, (180° * e), Putar], Rotate[C, 180°, Putar]) → C'
13. If(e ≤ 1, Rotate[D, (180° * e), Putar], Rotate[D, 180°, Putar]) → D'
14. If(e ≤ 1, Rotate[A, (180° * e), Putar], Rotate[A, 180°, Putar]) → A'
15. If(p ≟ true, Vector[C, D], Vector[D, C]) → u
16. Polygon(A', B', C', D') → poly1', a', b', c', d'
17. If(e > 1, Translate[A', Vector[((e - 1) * u)]]) → A''
18. If(e > 1, Translate[B', Vector[((e - 1) * u)]]) → B''
19. If(e > 1, Translate[C', Vector[((e - 1) * u)]]) → C''
20. If(e > 1, Translate[D', Vector[((e - 1) * u)]]) → D''
21. Polygon(A'', B'', C'', D'') → poly1'', a'', b'', c'', d''
22. Midpoint(B, C) → F
23. Midpoint(A, D) → G
24. Circle(F, ja) → f
25. Intersect(f, c) → I_2, I_1
26. Circle(I_1, ja) → k
27. Circle(I_2, ja) → p_2
28. Line(I_1, b) → j
29. Line(I_2, b) → g
30. Intersect(p_2, g, 2) → I_3
31. Intersect(k, j, 2) → I_4
32. Circle(C, ja) → q
33. Line(C, b) → i
34. Intersect(q, i, 2) → L
35. Circle(B, ja) → r
36. Line(B, b) → l
37. Intersect(r, l, 2) → M
38. Circle(G, ja) → s
39. Intersect(s, a) → P_4, P_3
40. Circle(P_3, ja) → t
41. Circle(P_4, ja) → d_1
42. Line(P_3, b) → h
43. Line(P_4, b) → m
44. Intersect(d_1, m, 1) → P_1
45. Intersect(t, h, 1) → P_2
46. Circle(D, ja) → e_1
47. Circle(A, ja) → f_1
48. Intersect(f_1, b, 1) → R
49. Line(D, b) → n
50. Intersect(e_1, n, 1) → S
51. Circle(E, ja) → g_1
52. Intersect(a, i) → T
53. Intersect(g_1, c, 1) → U
54. Intersect(f_1, a, 1) → V
55. Midpoint(E, A) → W
56. Circle(W, ja) → h_1
57. Intersect(h_1, b, 2) → Z
58. Intersect(h_1, b, 1) → A_1
59. Circle(Z, ja) → k_1
60. Circle(A_1, ja) → p_1
61. Line(Z, c) → i_1
62. Line(A_1, c) → j_1
63. Intersect(k_1, i_1, 1) → B_1
64. Intersect(p_1, j_1, 1) → C_1
65. Intersect(l, i_1) → D_1
66. Intersect(l, j_1) → E_1
67. Intersect(a, l) → F_1
68. Circle(D_1, ja) → q_1
69. Circle(E_1, ja) → r_1
70. Midpoint(F_1, B) → G_1
71. Intersect(r, c, 1) → H_1
72. Intersect(q_1, i_1, 1) → I_5
73. Intersect(r_1, j_1, 1) → J_1
74. Circle(F_1, ja) → s_1
75. Intersect(s_1, a, 1) → K_1
76. Intersect(r_1, j_1, 2) → I
77. Intersect(q_1, i_1, 2) → J
78. Intersect(s_1, a, 2) → K
79. Intersect(r, c, 2) → N
80. Intersect(k, j, 1) → O
81. Intersect(q, i, 1) → P
82. Intersect(p_2, g, 1) → Q
83. Intersect(r, l, 1) → L_1
84. If(p ≟ true, Vector[I_3, M], Vector[Q, L_1]) → v
85. If(p ≟ true, Vector[I_4, L], Vector[O, P]) → w
86. Intersect(f_1, b, 2) → M_1
87. Intersect(d_1, m, 2) → N_1
88. Intersect(t, h, 2) → O_1
89. Intersect(e_1, n, 2) → Q_1
90. If(p ≟ true, Vector[P_1, R], Vector[N_1, M_1]) → u_1
91. If(p ≟ true, Vector[P_2, S], Vector[O_1, Q_1]) → v_1
92. If(p ≟ true, Vector[B_1, V], Vector[C_1, V]) → w_1
93. If(p ≟ true, Vector[C_1, U], Vector[B_1, U]) → l_1
94. If(p ≟ true, Vector[J, K], Vector[I, K]) → m_1
95. If(p ≟ true, Vector[I, N], Vector[J, N]) → n_1
96. Angle(D, A, B) → α
97. Angle(C, B, A) → β
98. Angle(C, D, A) → γ
99. Angle(D, C, B) → δ
100. SelectedIndex(Bahasa) → nn
101. If(nn ≟ 1, "Derive the formula to calculate", "Menerbit rumus untuk menghitungkan") → Tex1
102. If(nn ≟ 1, "the area of a trapezium", "luas bentuk trapezium") → Tex2