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Pyramids in a Prism

Pyramids in a Prism
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2017-11-03 21:03
Solid GeometryTransformationGeometric Construction
This example demonstrates how to divide a prism into three pyramids. When the prism is a cube, it is clear that the pyramids are congruent. Through rotation and translation operations, the properties of the pyramids can be intuitively understood. This example involves concepts of geometric construction, prisms, and pyramids, suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Ray[A, A + (1, 0)]) → B
  3. Point(Ray[A, A + (0, 1)]) → C
  4. Translate(A, Vector[(0, 0, ht)]) → A'
  5. Translate(B, Vector[(0, 0, ht)]) → B'
  6. Translate(C, Vector[(0, 0, ht)]) → C'
  7. Translate(D, Vector[(0, 0, ht)]) → D'
  8. Segment(A, A') → a
  9. Segment(B, B') → b
  10. Segment(C, C') → c
  11. Segment(D, D') → d
  12. Segment(A, B) → e
  13. Segment(D, C) → f
  14. Segment(B, D) → g
  15. Segment(C, A) → h
  16. Segment(A', B') → i
  17. Segment(B', D') → j
  18. Segment(D', C') → k
  19. Segment(C', A') → l
  20. Pyramid(A, B, B', A', C') → m, faceAA'B'B, edgeAC'_1, edgeBC'_1, edgeB'C'_1, edgeA'C', faceABC'_1, faceBB'C'_1, faceA'B'C', faceAA'C', edgeAB_1, edgeBB'_1, edgeA'B', edgeAA'
  21. Pyramid(A, B, D, C, C') → n, faceABDC, edgeAC', edgeBC'_2, edgeC'D_1, edgeCC', faceABC', faceBC'D_1, faceCC'D, faceACC', edgeAB_2, edgeBD_1, edgeCD, edgeAC
  22. Pyramid(B, D, D', B', C') → o, faceBB'D'D, edgeBC', edgeC'D, edgeC'D', edgeB'C', faceBC'D, faceC'DD', faceB'C'D', faceBB'C', edgeBD_2, edgeDD', edgeB'D', edgeBB'
  23. Rotate
  24. Rotate
  25. Line(A, B) → q
  26. Rotate
  27. Rotate
  28. Rotate(A', ((decompose * 90))°, A, Vector[A, B]) → A''
  29. Rotate(B', ((decompose * 90))°, A, Vector[A, B]) → B''
  30. Rotate(C', ((decompose * 90))°, A, Vector[A, B]) → C''
  31. Pyramid(A, B, B'', A'', C'') → r, faceAA''B''B, edgeAC'', edgeBC'', edgeB''C'', edgeA''C'', faceABC'', faceBB''C'', faceA''B''C'', faceAA''C'', edgeAB, edgeBB'', edgeA''B'', edgeAA''
  32. Rotate(B', ((decompose * 90))°, B, Vector[B, D]) → B''_1
  33. Rotate(D', ((decompose * 90))°, B, Vector[B, D]) → D''
  34. Rotate(C', ((decompose * 90))°, B, Vector[B, D]) → C''_1
  35. Pyramid(B, D, D'', B''_1, C''_1) → s, face5, edge2, edge3, edge6, edge5, face1, face3, face4, face2, edgeBD, edgeDD'', edge4, edge1

AI Drawing Prompt Reference

Draw a right triangular prism and divide it into three pyramids. First, draw the base and sides of the prism, then extend three heights from the vertices of the base to form three pyramids. Finally, use rotation and translation operations to intuitively show the properties of the pyramids.
The prompt above was compiled from the original drawing commands and is for reference only.