三角形面积探究：从直角三角形到一般三角形的动态构造

GeoGebra 命令及参数

1. Line(A, B) → a
2. OrthogonalLine(A, a) → b
3. Point(b) → C
4. Line(C, a) → c
5. OrthogonalLine(B, a) → d
6. Intersect(c, d) → D
7. Segment(A, B) → e
8. Point(e) → E
9. Segment(E, C) → f
10. Segment(E, D) → g
11. Midpoint(f) → F
12. Midpoint(g) → G
13. Semicircle(E, D) → h
14. OrthogonalLine(E, e) → i
15. Intersect(c, i) → H
16. Semicircle(B, H) → k
17. Semicircle(D, E) → p_1
18. Semicircle(H, A) → q
19. Semicircle(C, E) → r
20. Semicircle(E, C) → s
21. Rotate(E, -α, G) → E'
22. Angle(E', G, E) → β
23. Rotate(B, -α, G) → B'
24. Angle(B', G, B) → γ
25. Rotate(D, -α, G) → D'
26. Angle(D', G, D) → δ
27. Polygon(E', B', D') → poly1, d', e', b'
28. Rotate(A, α, F) → A'
29. Angle(A, F, A') → ε
30. Rotate(E, α, F) → E'_1
31. Angle(E, F, E'_1) → ζ
32. Rotate(C, α, F) → C'
33. Angle(C, F, C') → η
34. Polygon(A', C', E'_1) → poly2, e'_1, a', c'
35. Midpoint(e) → I
36. Midpoint(A, C) → J
37. Midpoint(C, D) → K
38. Midpoint(B, D) → L
39. Polygon(J, I, L, K) → poly3, j_1, i_1, l, k_1
40. Midpoint(j_1) → M
41. Midpoint(i_1) → N
42. Midpoint(l) → O
43. Midpoint(k_1) → P
44. Rotate(J, α, P) → J'
45. Angle(J, P, J') → θ
46. Rotate(C, α, P) → C'_1
47. Angle(C, P, C'_1) → ι
48. Rotate(K, α, P) → K'
49. Angle(K, P, K') → κ
50. Polygon(J', C'_1, K') → poly4, k', j', c'_1
51. Rotate(K, -α, O) → K'_1
52. Angle(K'_1, O, K) → λ
53. Rotate(L, -α, O) → L'
54. Angle(L', O, L) → μ
55. Rotate(D, -α, O) → D'_1
56. Angle(D'_1, O, D) → ν
57. Polygon(K'_1, D'_1, L') → poly5, l', k'_1, d'_1
58. Rotate(A, -α, M) → A'_1
59. Angle(A'_1, M, A) → ξ
60. Rotate(I, -α, M) → I'
61. Angle(I', M, I) → ο
62. Rotate(J, -α, M) → J'_1
63. Angle(J'_1, M, J) → ρ
64. Polygon(J'_1, A'_1, I') → poly6, i', j'_1, a'_1
65. Rotate(B, α, N) → B'_1
66. Angle(B, N, B'_1) → σ
67. Rotate(L, α, N) → L'_1
68. Angle(L, N, L'_1) → τ
69. Rotate(I, α, N) → I'_1
70. Angle(I, N, I'_1) → υ
71. Polygon(B'_1, L'_1, I'_1) → poly7, i'_1, b'_1, l'_1
72. Segment(A', C') → n_2
73. Polygon(C, E, D) → poly8, d_1, c_1, e_1
74. Midpoint(A, C) → Q
75. Midpoint(D, C) → R
76. Midpoint(A, B) → S
77. Midpoint(B, D) → T
78. Segment(Q, T) → t
79. Segment(S, R) → a_1
80. Intersect(t, a_1) → U
81. Point(e) → V
82. Mirror(V, U) → V'
83. Polygon(C, Q, V, B, T, V') → poly9, c_2, q_1, v, b_1, t_1, v'
84. Rotate(A, α, Q) → A'_2
85. Angle(A, Q, A'_2) → ϕ
86. Rotate(V, α, Q) → V'_1
87. Angle(V, Q, V'_1) → χ
88. Polygon(Q, V'_1, A'_2) → poly10, a'_2, q_2, v'_1
89. Rotate(V', α, T) → V''
90. Angle(V', T, V'') → ψ
91. Rotate(D, α, T) → D'_2
92. Angle(D, T, D'_2) → ω
93. Polygon(V'', D'_2, T) → poly11, t_2, v'', d'_2
94. Segment(C, D) → f_1
95. Segment(C, V') → g_1
96. Segment(V, B) → h_1
97. Segment(Q, C) → l_1
98. Midpoint(A, C) → W
99. Midpoint(B, D) → Z
100. Segment(V, B) → m_1
101. Point(m_1) → A_1
102. Polygon(W, C, D, Z, A_1, V) → poly12, w, c_3, d_2, z, u_2, v_1
103. Rotate(A_1, -α, Z) → B_1
104. Angle(B_1, Z, A_1) → α_1
105. Rotate(B, -α, Z) → B'_2
106. Angle(B'_2, Z, B) → β_1
107. Polygon(B_1, Z, B'_2) → poly13, b'_2, b_2, z_1
108. Segment(E, C) → n_1
109. Segment(C, D) → r_1
110. Segment(E, D) → s_1
111. Midpoint(s_1) → C_1
112. Rotate(E, α, C_1) → E'_2
113. Angle(E, C_1, E'_2) → γ_1
114. Rotate(C, α, C_1) → C'_2
115. Angle(C, C_1, C'_2) → δ_1
116. Rotate(D, α, C_1) → D'_3
117. Angle(D, C_1, D'_3) → ε_1
118. Polygon(E'_2, C'_2, D'_3) → poly14, d'_3, e'_2, c'_2
119. Midpoint(A, C) → D_1
120. Midpoint(B, D) → E_1
121. Mirror(V, D_1) → V'_2
122. Mirror(A_1, E_1) → F_1
123. Polygon(V, V'_2, F_1, A_1) → poly15, v_2, v'_2, f_2, a_2
124. Midpoint(A_1, F_1) → G_1
125. Rotate(A_1, α, G_1) → H_1
126. Angle(A_1, G_1, H_1) → ζ_1
127. Rotate(V, α, G_1) → V'_3
128. Angle(V, G_1, V'_3) → η_1
129. Rotate(V'_2, α, G_1) → I_1
130. Angle(V'_2, G_1, I_1) → θ_1
131. Rotate(F_1, α, G_1) → J_1
132. Angle(F_1, G_1, J_1) → ι_1
133. Polygon(V'_3, I_1, J_1, H_1) → poly16, v'_3, i_2, j_2, h_2
134. Polygon(E'_1, A', C') → poly17, c'_3, e'_3, a'_3
135. Polygon(A, C, D, B) → poly18, a_3, c_4, d_3, b_3
136. Polygon(C, E, D) → poly19, d_4, c_5, e_2
137. Polygon(E', B', D') → poly20, d'_4, e'_4, b'_3
138. Polygon(A'_1, J'_1, I') → poly21, i'_2, a'_4, j'_2
139. Polygon(B'_1, I'_1, L'_1) → poly22, l'_2, b'_4, i'_3
140. Polygon(J', K', C'_1) → poly23, c'_4, j'_3, k'_2
141. Polygon(K'_1, D'_1, L') → poly24, l'_3, k'_3, d'_5
142. Polygon(A, C, D, B) → poly25, a_4, c_6, d_5, b_4
143. Polygon(I, J, K, L) → poly26, i_3, j_3, k_2, l_2
144. Polygon(V'_1, A'_2, Q) → poly27, q_3, v'_4, a'_5
145. Polygon(D'_2, T, V'') → poly28, v''_1, d'_6, t_3
146. Polygon(V, V'_1, V', V'') → poly29, v_3, v'_5, v'_6, v''_2
147. Polygon(A, C, D, B) → poly30, a_5, c_7, d_6, b_5
148. Point(b_5) → K_1
149. Polygon(V'_1, A'_2, Q) → poly31, q_4, v'_7, a'_6
150. Polygon(B_1, Z, B'_2) → poly32, b'_5, b_6, z_2
151. Polygon(V, V'_1, B_1, A_1) → poly33, v_4, v'_8, b_7, a_6
152. Polygon(A, C, D, B) → poly34, a_7, c_8, d_7, b_8
153. Polygon(E, C, D) → poly35, d_8, e_3, c_9
154. Polygon(D'_3, E'_2, C'_2) → poly36, c'_5, d'_7, e'_5
155. Polygon(C'_2, E, C, D) → poly37, c'_6, e_4, c_{10}, d_9
156. Polygon(V, V'_2, F_1, A_1) → poly38, v_5, v'_9, f_3, a_8
157. Polygon(J_1, H_1, V'_3, I_1) → poly39, j_4, h_3, v'_{10}, i_4
158. Polygon(V, V'_2, V'_3, I_1) → poly40, v_6, v'_{11}, v'_{12}, i_5