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棱柱的三视图绘制

棱柱的三视图绘制
几何画板及绘图内容加载中，请稍等……
2018-04-18 05:35
解析几何立体几何几何作图
所属专题 Cuboids & their Nets
①本范例演示棱柱的三视图（主视图、俯视图、侧视图）绘制方法；②涉及的核心数学概念包括立体几何、几何作图、空间想象能力；③作图要点提炼自构造摘要，使用了点(Point)、线段(Segment)、取点(Take)、多边形(Polygon)等GeoGebra命令，以及点击点(ClickedPoints)、特定点(S, O, N, M)、按钮(B, C, D, E, F, G, H, K, L, P, Q, R, T, U, V, W, Z, B_1, D_1, M_1, L1, L2, L3, L4, L5, L6, L7, L8, L9, L10)等对象；④适合初中及以上学段，用于几何教学和空间几何能力培养。

GeoGebra 命令及参数

  1. Point(yAxis) → D_1
  2. Segment(Element[ClickedPoints, 1], Element[ClickedPoints, 2]) → L1
  3. Segment(Element[ClickedPoints, 3], Element[ClickedPoints, 4]) → L2
  4. Segment(Element[ClickedPoints, 5], Element[ClickedPoints, 6]) → L3
  5. Segment(Element[ClickedPoints, 7], Element[ClickedPoints, 8]) → L4
  6. Segment(Element[ClickedPoints, 9], Element[ClickedPoints, 10]) → L5
  7. Segment(Element[ClickedPoints, 11], Element[ClickedPoints, 12]) → L6
  8. Segment(Element[ClickedPoints, 13], Element[ClickedPoints, 14]) → L7
  9. Segment(Element[ClickedPoints, 15], Element[ClickedPoints, 16]) → L8
  10. Segment(Element[ClickedPoints, 17], Element[ClickedPoints, 18]) → L9
  11. Segment(Element[ClickedPoints, 19], Element[ClickedPoints, 20]) → L10
  12. Take(ClickedPoints, 1, NumClicks) → ShortPointList
  13. Take(LineList, 1, NumLines) → ShortLineList
  14. Segment(Element[ClickedPoints, 21], Element[ClickedPoints, 22]) → L11
  15. Segment(Element[ClickedPoints, 23], Element[ClickedPoints, 24]) → L12
  16. Segment(Element[ClickedPoints, 25], Element[ClickedPoints, 26]) → L13
  17. Segment(Element[ClickedPoints, 27], Element[ClickedPoints, 28]) → L14
  18. Segment(Element[ClickedPoints, 29], Element[ClickedPoints, 30]) → L15
  19. Segment(Element[ClickedPoints, 31], Element[ClickedPoints, 32]) → L16
  20. Segment(Element[ClickedPoints, 33], Element[ClickedPoints, 34]) → L17
  21. Segment(Element[ClickedPoints, 35], Element[ClickedPoints, 36]) → L18
  22. Segment(Element[ClickedPoints, 37], Element[ClickedPoints, 38]) → L19
  23. Segment(Element[ClickedPoints, 39], Element[ClickedPoints, 40]) → L20
  24. Segment(Q14, Q30) → P1line1
  25. Segment(Q44, Q30) → P1line2
  26. Segment(Q28, Q44) → P1line3
  27. Segment(Q28, Q14) → P1line4
  28. Segment(Q14, Q7) → P1line5
  29. Segment(Q7, Q21) → P1line6
  30. Segment(Q21, Q28) → P1line7
  31. Segment(Q21, Q37) → P1line8
  32. Segment(Q37, Q44) → P1line9
  33. Polygon(Q14, Q28, Q44, Q30) → P1Front, q14, q28, q44, q30
  34. Polygon(Q28, Q21, Q37, Q44) → P1Side, q28_1, q21, q37, q44_1
  35. Polygon(Q14, Q7, Q21, Q28) → P1Top, q14_1, q7, q21_1, q28_2
  36. Polygon((-0.5, 5.5), (4.5, 5.5), (4.5, -0.5), (-0.5, -0.5)) → PaperOutline, f, g, h, i
  37. Segment(A7, A10) → P1front1
  38. Segment(A10, A20) → P1front2
  39. Segment(A20, A17) → P1front3
  40. Segment(A17, A7) → P1front4
  41. Polygon(A7, A10, A20, A17) → P1FrontA, a7, a10, a20, a17
  42. Polygon(A7, A10, A20, A17) → P1TopA, a7_1, a10_1, a20_1, a17_1
  43. Segment(A7, A17) → P1side1
  44. Segment(A17, A19) → P1side2
  45. Segment(A19, A9) → P1side3
  46. Segment(A9, A7) → P1side4
  47. Polygon(A7, A9, A19, A17) → P1SideA, a7_2, a9, a19, a17_2
  48. Segment(Q22, Q38) → P2line9
  49. Segment(Q38, Q43) → P2line1
  50. Segment(Q22, Q27) → P2line4
  51. Segment(Q27, Q43) → P2line5
  52. Segment(Q22, Q8) → P2line2
  53. Segment(Q8, Q13) → P2line3
  54. Segment(Q13, Q27) → P2line6
  55. Segment(Q13, Q29) → P2line7
  56. Segment(Q29, Q43) → P2line8
  57. Polygon(Q38, Q22, Q27, Q43) → P2Front, q38, q22, q27, q43
  58. Polygon(Q27, Q13, Q29, Q43) → P2Side, q27_1, q13, q29, q43_1
  59. Polygon(Q22, Q8, Q13, Q27) → P2Top, q22_1, q8, q13_1, q27_2
  60. Segment(A6, A10) → P2top1
  61. Segment(A10, A15) → P2top2
  62. Segment(A15, A11) → P2top3
  63. Segment(A11, A6) → P2top4
  64. Polygon(A6, A10, A15, A11) → P2TopA, a6, a10_2, a15, a11
  65. Segment(A6, A10) → P2side1
  66. Segment(A10, A20) → P2side2
  67. Segment(A20, A16) → P2side3
  68. Segment(A16, A6) → P2side4
  69. Polygon(A6, A10, A20, A16) → P2SideA, a6_1, a10_3, a20_2, a16
  70. Segment(A7, A17) → P2front1
  71. Segment(A17, A18) → P2front4
  72. Segment(A18, A8) → P2front3
  73. Segment(A8, A7) → P2front2
  74. Polygon(A7, A8, A18, A17) → P2FrontA, a7_3, a8, a18, a17_3
  75. Segment(Q3, Q11) → P3line1
  76. Segment(Q11, Q20) → P3line2
  77. Segment(Q20, Q13) → P3line3
  78. Segment(Q13, Q3) → P3line8
  79. Segment(Q13, Q29) → P3line4
  80. Segment(Q29, Q36) → P3line9
  81. Segment(Q36, Q27) → P3line5
  82. Segment(Q27, Q11) → P3line6
  83. Segment(Q20, Q36) → P3line7
  84. Polygon(Q27, Q11, Q20, Q36) → P3Front, q27_3, q11, q20, q36
  85. Polygon(Q20, Q13, Q29, Q36) → P3Side, q20_1, q13_2, q29_1, q36_1
  86. Polygon(Q11, Q3, Q13, Q20) → P3Top, q11_1, q3, q13_3, q20_2
  87. Segment(A7, A9) → P3front2
  88. Segment(A19, A9) → P3front3
  89. Segment(A19, A17) → P3front4
  90. Segment(A17, A7) → P3front1
  91. Polygon(A7, A9, A19, A17) → P3TopA, a7_4, a9_1, a19_1, a17_4
  92. Polygon(A7, A9, A19, A17) → P3FrontA, a7_5, a9_2, a19_2, a17_5
  93. Polygon(A7, A9, A19, A17) → P3SideA, a7_6, a9_3, a19_3, a17_6
  94. Segment(Q29, Q39) → P4line1
  95. Segment(Q39, Q30) → P4line2
  96. Segment(Q30, Q22) → P4line3
  97. Segment(Q22, Q31) → P4line4
  98. Segment(Q31, Q39) → P4line5
  99. Segment(Q22, Q12) → P4line6
  100. Segment(Q12, Q21) → P4line7
  101. Segment(Q21, Q29) → P4line8
  102. Segment(Q21, Q31) → P4line9
  103. Polygon(Q22, Q12, Q21, Q31) → P4Top, q22_2, q12, q21_2, q31
  104. Polygon(Q22, Q31, Q39, Q30) → P4Front, q22_3, q31_1, q39, q30_1
  105. Polygon(Q39, Q31, Q21, Q29) → P4Side, q39_1, q31_2, q21_3, q29_2
  106. Segment(A7, A10) → P4top1
  107. Segment(A10, A20) → P4top2
  108. Segment(A20, A17) → P4top3
  109. Segment(A17, A7) → P4top4
  110. Polygon(A7, A10, A20, A17) → P4TopA, a7_7, a10_4, a20_3, a17_7
  111. Segment(A7, A10) → P4side2
  112. Segment(A10, A15) → P4side3
  113. Segment(A15, A12) → P4side4
  114. Segment(A12, A7) → P4side1
  115. Polygon(A7, A10, A15, A12) → P4SideA, a7_8, a10_5, a15_1, a12
  116. Segment(A7, A12) → P4front4
  117. Segment(A12, A14) → P4front3
  118. Segment(A14, A9) → P4front2
  119. Segment(A9, A7) → P4front1
  120. Polygon(A7, A9, A14, A12) → P4FrontA, a7_9, a9_4, a14, a12_1
  121. Segment(Q39, Q25) → P5line1
  122. Segment(Q25, Q17) → P5line2
  123. Segment(Q17, Q3) → P5line3
  124. Segment(Q3, Q18) → P5line4
  125. Segment(Q18, Q31) → P5line6
  126. Segment(Q31, Q39) → P5line7
  127. Segment(Q39, Q26) → P5line8
  128. Segment(Q26, Q18) → P5line9
  129. Segment(Q31, Q17) → P5line5
  130. Polygon(Q18, Q26, Q39, Q31) → P5Front, q18, q26, q39_2, q31_3
  131. Polygon(Q31, Q39, Q25, Q17) → P5Side, q31_4, q39_3, q25, q17
  132. Polygon(Q18, Q3, Q17, Q31) → P5Top, q18_1, q3_1, q17_1, q31_5
  133. Segment(A6, A10) → P5top1
  134. Segment(A10, A25) → P5top2
  135. Segment(A25, A21) → P5top3
  136. Segment(A21, A6) → P5top4
  137. Polygon(A6, A10, A25, A21) → P5TopA, a6_2, a10_6, a25, a21
  138. Segment(A7, A10) → P5front1
  139. Segment(A10, A15) → P5front2
  140. Segment(A15, A12) → P5front3
  141. Segment(A12, A7) → P5front4
  142. Polygon(A7, A10, A15, A12) → P5FrontA, a7_{10}, a10_7, a15_2, a12_2
  143. Segment(A6, A10) → P5side1
  144. Segment(A10, A15) → P5side2
  145. Segment(A15, A11) → P5side3
  146. Segment(A11, A6) → P5side4
  147. Polygon(A6, A10, A15, A11) → P5SideA, a6_3, a10_8, a15_3, a11_1
  148. Segment(Q30, Q44) → P6line3
  149. Segment(Q44, Q40) → P6line4
  150. Segment(Q40, Q16) → P6line5
  151. Segment(Q16, Q20) → P6line6
  152. Segment(Q20, Q6) → P6line7
  153. Segment(Q6, Q30) → P6line2
  154. Segment(Q6, Q2) → P6line1
  155. Segment(Q2, Q16) → P6line8
  156. Segment(Q20, Q44) → P6line9
  157. Polygon(Q6, Q20, Q44, Q30) → P6Front, q6, q20_3, q44_2, q30_2
  158. Polygon(Q20, Q16, Q40, Q44) → P6Side, q20_4, q16, q40, q44_3
  159. Polygon(Q6, Q2, Q16, Q20) → P6Top, q6_1, q2, q16_1, q20_5
  160. Segment(A7, A22) → P6side4
  161. Segment(A22, A23) → P6side3
  162. Segment(A23, A8) → P6side2
  163. Segment(A8, A7) → P6side1
  164. Polygon(A7, A8, A23, A22) → P6SideA, a7_{11}, a8_1, a23, a22
  165. Segment(A7, A22) → P6front4
  166. Segment(A22, A25) → P6front3
  167. Segment(A25, A10) → P6front2
  168. Segment(A10, A7) → P6front1
  169. Polygon(A7, A10, A25, A22) → P6FrontA, a7_{12}, a10_9, a25_1, a22_1
  170. Segment(A7, A12) → P6top1
  171. Segment(A12, A15) → P6top4
  172. Segment(A15, A10) → P6top3
  173. Segment(A10, A7) → P6top2
  174. Polygon(A7, A10, A15, A12) → P6TopA, a7_{13}, a10_{10}, a15_4, a12_3