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Drawing Views of Composite Prisms

Drawing Views of Composite Prisms
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2018-04-19 22:26
Solid GeometryGeometric ConstructionGraphing
In collections Cuboids & their Nets
This example demonstrates how to draw the three views of composite prisms. It involves core mathematical concepts such as prisms, three-view projections, and geometric constructions. The construction uses basic elements like points, segments, and polygons, along with operations like taking points and constructing lines. Suitable for middle school students and above learning solid geometry and geometric constructions.

GeoGebra Commands & Parameters

  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. Polygon((-0.5, 5.5), (4.5, 5.5), (4.5, -0.5), (-0.5, -0.5)) → PaperOutline, f, g, h, i
  25. Segment(Q35, Q43) → P1line4
  26. Segment(Q43, Q38) → P1line5
  27. Segment(Q38, Q30) → P1line6
  28. Segment(Q30, Q35) → P1line7
  29. Segment(Q35, Q21) → P1line8
  30. Segment(Q21, Q29) → P1line9
  31. Segment(Q29, Q43) → P1line10
  32. Segment(Q30, Q23) → P1line11
  33. Segment(Q21, Q7) → P1line12
  34. Segment(Q7, Q14) → P1line13
  35. Segment(Q14, Q23) → P1line1
  36. Segment(Q14, Q22) → P1line2
  37. Segment(Q22, Q27) → P1line3
  38. Polygon(Q14, Q7, Q21, Q35, Q30, Q23) → P1Top, q14, q7, q21, q35, q30, q23
  39. Polygon(Q35, Q21, Q29, Q43) → P1Side, q35_1, q21_1, q29, q43
  40. Polygon(Q30, Q35, Q43, Q38) → P1Front1, q30_1, q35_2, q43_1, q38
  41. Polygon(Q14, Q23, Q27, Q22) → P1Front2, q14_1, q23_1, q27, q22
  42. Segment(A7, A10) → P1front1
  43. Segment(A10, A15) → P1front2
  44. Segment(A15, A12) → P1front3
  45. Segment(A12, A7) → P1front4
  46. Segment(A9, A14) → P1front5
  47. Polygon(A9, A10, A15, A14) → P1Front1A, a9, a10, a15, a14
  48. Polygon(A7, A9, A14, A12) → P1Front2A, a7, a9_1, a14_1, a12
  49. Segment(A21, A25) → P1top1
  50. Segment(A25, A10) → P1top2
  51. Segment(A10, A8) → P1top3
  52. Segment(A8, A18) → P1top4
  53. Segment(A18, A16) → P1top5
  54. Segment(A16, A21) → P1top6
  55. Polygon(A16, A18, A8, A10, A25, A21) → P1TopA, a16, a18, a8, a10_1, a25, a21
  56. Segment(A11, A15) → P1side1
  57. Segment(A15, A10) → P1side2
  58. Segment(A10, A6) → P1side3
  59. Segment(A6, A11) → P1side4
  60. Polygon(A6, A10, A15, A11) → P1SideA, a6, a10_2, a15_1, a11
  61. Segment(Q44, Q33) → P2line2
  62. Segment(Q33, Q17) → P2line3
  63. Segment(Q44, Q30) → P2line6
  64. Segment(Q44, Q36) → P2line7
  65. Segment(Q36, Q32) → P2line8
  66. Segment(Q32, Q24) → P2line4
  67. Segment(Q24, Q17) → P2line5
  68. Segment(Q36, Q22) → P2line9
  69. Segment(Q22, Q30) → P2line10
  70. Segment(Q22, Q19) → P2line11
  71. Segment(Q19, Q11) → P2line12
  72. Segment(Q11, Q24) → P2line13
  73. Segment(Q19, Q32) → P2line14
  74. Segment(Q11, Q3) → P2line15
  75. Segment(Q3, Q17) → P2line1
  76. Polygon(Q11, Q3, Q17, Q24) → P2Top1, q11, q3, q17, q24
  77. Polygon(Q19, Q22, Q36, Q32) → P2Top2, q19, q22_1, q36, q32
  78. Polygon(Q22, Q30, Q44, Q36) → P2Front1, q22_2, q30_2, q44, q36_1
  79. Polygon(Q11, Q19, Q32, Q24) → P2Front2, q11_1, q19_1, q32_1, q24_1
  80. Polygon(Q44, Q36, Q32, Q24, Q17, Q33) → P2Side, q44_1, q36_2, q32_2, q24_2, q17_1, q33
  81. Segment(A17, A20) → P2side1
  82. Segment(A20, A10) → P2side2
  83. Segment(A10, A8) → P2side3
  84. Segment(A8, A13) → P2side4
  85. Segment(A13, A12) → P2side5
  86. Segment(A12, A17) → P2side6
  87. Polygon(A12, A13, A8, A10, A20, A17) → P2SideA, a12_1, a13, a8_1, a10_3, a20, a17
  88. Segment(A7, A10) → P2top1
  89. Segment(A10, A20) → P2top2
  90. Segment(A20, A17) → P2top3
  91. Segment(A17, A7) → P2top4
  92. Segment(A17, A22) → P2top5
  93. Segment(A22, A25) → P2top6
  94. Segment(A25, A20) → P2top7
  95. Polygon(A7, A10, A20, A17) → P2Top1A, a7_1, a10_4, a20_1, a17_1
  96. Polygon(A22, A25, A20, A17) → P2Top2A, a22, a25_1, a20_2, a17_2
  97. Segment(A17, A20) → P2front1
  98. Segment(A20, A10) → P2front2
  99. Segment(A10, A7) → P2front3
  100. Segment(A7, A17) → P2front4
  101. Segment(A12, A15) → P2front5
  102. Polygon(A12, A15, A20, A17) → P2Front1A, a12_2, a15_2, a20_3, a17_3
  103. Polygon(A7, A10, A15, A12) → P2Front2A, a7_2, a10_5, a15_3, a12_3
  104. Segment(Q26, Q30) → P3line4
  105. Segment(Q30, Q38) → P3line5
  106. Segment(Q38, Q34) → P3line6
  107. Segment(Q34, Q26) → P3line7
  108. Segment(Q30, Q16) → P3line8
  109. Segment(Q16, Q12) → P3line9
  110. Segment(Q12, Q26) → P3line10
  111. Segment(Q28, Q38) → P3line11
  112. Segment(Q28, Q44) → P3line12
  113. Segment(Q44, Q39) → P3line13
  114. Segment(Q39, Q31) → P3line2
  115. Segment(Q16, Q40) → P3line3
  116. Segment(Q40, Q44) → P3line1
  117. Polygon(Q26, Q30, Q16, Q12) → P3Top, q26, q30_3, q16, q12
  118. Polygon(Q30, Q16, Q40, Q44, Q28, Q38) → P3Side, q30_4, q16_1, q40, q44_2, q28, q38_1
  119. Polygon(Q26, Q30, Q38, Q34) → P3Front1, q26_1, q30_5, q38_2, q34
  120. Polygon(Q31, Q28, Q44, Q39) → P3Front2, q31, q28_1, q44_3, q39
  121. Segment(A6, A10) → P3side1
  122. Segment(A10, A25) → P3side2
  123. Segment(A25, A24) → P3side3
  124. Segment(A24, A14) → P3side4
  125. Segment(A14, A11) → P3side5
  126. Segment(A11, A6) → P3side6
  127. Polygon(A6, A10, A25, A24, A14, A11) → P3SideA, a6_1, a10_6, a25_2, a24, a14_2, a11_1
  128. Segment(A6, A10) → P3top1
  129. Segment(A10, A15) → P3top2
  130. Segment(A15, A11) → P3top3
  131. Segment(A11, A6) → P3top4
  132. Polygon(A6, A10, A15, A11) → P3TopA, a6_2, a10_7, a15_4, a11_2
  133. Segment(A7, A22) → P3front1
  134. Segment(A22, A23) → P3front2
  135. Segment(A23, A8) → P3front3
  136. Segment(A8, A7) → P3front4
  137. Segment(A12, A13) → P3front5
  138. Polygon(A7, A8, A13, A12) → P3Front1A, a7_3, a8_2, a13_1, a12_4
  139. Polygon(A12, A13, A23, A22) → P3Front2A, a12_5, a13_2, a23, a22_1
  140. Segment(Q25, Q29) → P4line9
  141. Segment(Q37, Q33) → P4line10
  142. Segment(Q33, Q25) → P4line11
  143. Segment(Q29, Q32) → P4line12
  144. Segment(Q32, Q40) → P4line13
  145. Segment(Q37, Q40) → P4line14
  146. Segment(Q40, Q31) → P4line15
  147. Segment(Q31, Q35) → P4line16
  148. Segment(Q35, Q26) → P4line17
  149. Segment(Q23, Q32) → P4line1
  150. Segment(Q23, Q31) → P4line2
  151. Segment(Q23, Q27) → P4line3
  152. Segment(Q27, Q18) → P4line4
  153. Segment(Q18, Q26) → P4line5
  154. Segment(Q27, Q35) → P4line6
  155. Segment(Q25, Q7) → P4line7
  156. Segment(Q7, Q18) → P4line8
  157. Polygon(Q18, Q7, Q25, Q32, Q23, Q27) → P4Top, q18, q7_1, q25, q32_3, q23_2, q27_1
  158. Polygon(Q18, Q27, Q35, Q26) → P4Front1, q18_1, q27_2, q35_3, q26_2
  159. Polygon(Q23, Q32, Q40, Q31) → P4Front2, q23_3, q32_4, q40_1, q31_1
  160. Polygon(Q32, Q25, Q33, Q40) → P4Side1, q32_5, q25_1, q33_1, q40_2
  161. Polygon(Q27, Q23, Q31, Q35) → P4Side2, q27_3, q23_4, q31_2, q35_4
  162. Segment(A6, A10) → P4top1
  163. Segment(A10, A20) → P4top2
  164. Segment(A20, A18) → P4top3
  165. Segment(A18, A23) → P4top4
  166. Segment(A23, A21) → P4top5
  167. Segment(A21, A6) → P4top6
  168. Polygon(A6, A10, A20, A18, A23, A21) → P4TopA, a6_3, a10_8, a20_4, a18_1, a23_1, a21_1
  169. Segment(A6, A11) → P4front1
  170. Segment(A11, A15) → P4front2
  171. Segment(A15, A10) → P4front3
  172. Segment(A10, A6) → P4front4
  173. Segment(A8, A13) → P4front5
  174. Polygon(A8, A13, A11, A6) → P4Front1A, a8_3, a13_3, a11_3, a6_4
  175. Polygon(A8, A13, A15, A10) → P4Front2A, a8_4, a13_4, a15_5, a10_9
  176. Segment(A7, A12) → P4side1
  177. Segment(A12, A15) → P4side2
  178. Segment(A15, A10) → P4side3
  179. Segment(A10, A7) → P4side4
  180. Segment(A8, A13) → P4side5
  181. Polygon(A8, A13, A15, A10) → P4Side1A, a8_5, a13_5, a15_6, a10_{10}
  182. Polygon(A8, A13, A12, A7) → P4Side2A, a8_6, a13_6, a12_6, a7_4
  183. Segment(Q33, Q44) → P5line8
  184. Segment(Q36, Q25) → P5line13
  185. Segment(Q25, Q33) → P5line14
  186. Segment(Q36, Q44) → P5line15
  187. Segment(Q25, Q21) → P5line16
  188. Segment(Q21, Q13) → P5line17
  189. Segment(Q21, Q28) → P5line18
  190. Segment(Q20, Q13) → P5line3
  191. Segment(Q13, Q3) → P5line4
  192. Segment(Q3, Q11) → P5line5
  193. Segment(Q11, Q19) → P5line6
  194. Segment(Q19, Q22) → P5line7
  195. Segment(Q22, Q30) → P5line9
  196. Segment(Q11, Q20) → P5line10
  197. Segment(Q20, Q28) → P5line11
  198. Segment(Q28, Q19) → P5line12
  199. Segment(Q22, Q36) → P5line1
  200. Segment(Q44, Q30) → P5line2
  201. Polygon(Q11, Q3, Q13, Q20) → P5Top1, q11_2, q3_1, q13, q20
  202. Polygon(Q19, Q22, Q36, Q25, Q21, Q28) → P5Top2, q19_2, q22_3, q36_3, q25_2, q21_2, q28_2
  203. Polygon(Q22, Q36, Q44, Q30) → P5Front1, q22_4, q36_4, q44_4, q30_6
  204. Polygon(Q11, Q20, Q28, Q19) → P5Front2, q11_3, q20_1, q28_3, q19_3
  205. Polygon(Q20, Q13, Q21, Q28) → P5Side2, q20_2, q13_1, q21_3, q28_4
  206. Polygon(Q36, Q25, Q33, Q44) → P5Side1, q36_5, q25_3, q33_2, q44_5
  207. Segment(A12, A15) → P5front1
  208. Segment(A15, A20) → P5front2
  209. Segment(A20, A17) → P5front3
  210. Segment(A17, A12) → P5front4
  211. Segment(A12, A7) → P5front5
  212. Segment(A7, A9) → P5front6
  213. Segment(A9, A14) → P5front7
  214. Polygon(A12, A15, A20, A17) → P5Front1A, a12_7, a15_7, a20_5, a17_4
  215. Polygon(A12, A14, A9, A7) → P5Front2A, a12_8, a14_3, a9_2, a7_5
  216. Segment(A12, A15) → P5side1
  217. Segment(A15, A20) → P5side2
  218. Segment(A20, A17) → P5side3
  219. Segment(A17, A12) → P5side4
  220. Segment(A13, A8) → P5side5
  221. Segment(A8, A10) → P5side6
  222. Segment(A10, A15) → P5side7
  223. Polygon(A12, A15, A20, A17) → P5Side1A, a12_9, a15_8, a20_6, a17_5
  224. Polygon(A13, A15, A10, A8) → P5Side2A, a13_7, a15_9, a10_{11}, a8_7
  225. Segment(A7, A10) → P5top1
  226. Segment(A10, A25) → P5top2
  227. Segment(A25, A22) → P5top3
  228. Segment(A22, A7) → P5top4
  229. Segment(A9, A19) → P5top5
  230. Segment(A19, A17) → P5top6
  231. Polygon(A7, A9, A19, A17) → P5Top1A, a7_6, a9_3, a19, a17_6
  232. Polygon(A9, A10, A25, A22, A17, A19) → P5Top2A, a9_4, a10_{12}, a25_3, a22_2, a17_7, a19_1