MathPlotAI Logo MathPlotAI

Section of a Right Prism by a Plane Parallel to Its Base

Section of a Right Prism by a Plane Parallel to Its Base
Loading the math board and drawing, please wait…
2012-11-14 03:25
PolygonVectorSolid GeometryMatrixGeometric Construction
This GeoGebra example demonstrates the cross-section of a right prism (pavé droit) cut by a plane parallel to its base, illustrating that the section is congruent to the base and its position can be varied. Core mathematical concepts include solid geometry, prism sections, parallel planes, congruent polygons, and spatial relationships among points, lines, and planes. The construction uses GeoGebra commands Sequence, Element, Point, Polygon, and Segment, together with objects such as cube, droite, listepoints, poly1, and transformation objects Mat, R_x, R_y to build prism vertices and generate the section polygon. Suitable for middle and high school solid geometry instruction, classroom demonstrations, and student exploration of parallel cross-section properties.

GeoGebra Commands & Parameters

  1. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
  2. Element(Element[AE, 3], 1) → droite
  3. Sequence((Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  4. Point(listepoints) → A
  5. Point(listepoints) → E
  6. Point(listepoints) → C_1
  7. Point(listepoints) → D
  8. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
  9. Point(listepoints) → B
  10. Point(listepoints) → F
  11. Point(listepoints) → G
  12. Point(listepoints) → H
  13. Polygon(B, F, G, H) → poly2, e, f, g, h
  14. Point(listepoints) → C
  15. Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
  16. Element(AB, 3, 1) → avant
  17. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
  18. Element(AC, 3, 1) → dessus
  19. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
  20. Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
  21. Segment(E, A) → c
  22. Segment(A, C) → j
  23. Segment(A, B) → k
  24. Segment(C, C_1) → l
  25. Segment(C_1, E) → m
  26. Segment(H, E) → n
  27. Segment(A, B) → p
  28. Segment(B, H) → q
  29. Segment(H, E) → r
  30. Segment(H, G) → s
  31. Segment(B, F) → t
  32. Segment(G, C_1) → d_1
  33. Segment(F, G) → i_1
  34. Segment(F, C) → j_1
  35. Sequence(Mat * Element[plan, k], k, 1, 4) → plan'
  36. Sequence((Element[plan', k, 1, 1], Element[plan', k, 2, 1]), k, 1, 4) → listepoints2
  37. Point(listepoints2) → M
  38. Point(listepoints2) → N
  39. Point(listepoints2) → Q
  40. Point(listepoints2) → R
  41. Polygon(M, N, Q, R) → poly7, m_2, n_2, q_2, r_1
  42. Polygon(Translate[A, Vector[(u - w) / (2 * w) * Vector[G, H]]], Translate[B, Vector[(u - w) / (2 * w) * Vector[G, H]]], Translate[H, Vector[(u - w) / (2 * w) * Vector[G, H]]], Translate[E, Vector[(u - w) / (2 * w) * Vector[G, H]]]) → poly', k_1, l_1, m_1, n_1

AI Drawing Prompt Reference

Please draw a cross-section of a right prism cut by a plane parallel to its base. First, construct a cube as the basis for the right prism, then determine points on the sectioning plane. Use these points to draw the section polygon and show its relationship with the original base. The final figure should include the cube, the sectioning plane, and the section polygon, demonstrating the congruence of the section with the base and its positional variation.
The prompt above was compiled from the original drawing commands and is for reference only.