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Prism and Special Points Demonstration

Prism and Special Points Demonstration
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2020-04-30 16:37
PolygonSolid GeometryGeometric ConstructionLocus
This example demonstrates the geometric relationships of a right prism, its lateral faces, vertices, edges, and special points. Key math concepts include solid geometry, polygons, special points (e.g., midpoints of edges, angle bisectors), and locus. Construction involves commands like Intersect, Point, Polygon, Prism, Line, CircleArc, Segment, Locus, Rotate, LineBisector, Plane, and Mirror. Suitable for high school geometry instruction and construction exploration.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, yAxis) → B
  2. Point(xAxis) → C
  3. Point(yAxis) → D
  4. Polygon(B, C, A, D) → vierhoek1, b, c, a, d
  5. Prism(vierhoek1, 2) → e, E, RibbeBE, RibbeCF, RibbeAG, RibbeDH, RibbeEF, RibbeFG, RibbeGH, RibbeEH, F, G, H, zijvlakBCFE, zijvlakACFG, zijvlakADHG, zijvlakBDHE, zijvlakEFGH
  6. Point(zAxis) → I
  7. Line(M, N) → f
  8. CircleArc(M, J, L) → g
  9. Line(M, I) → h
  10. Segment(J, F) → i
  11. Segment(L, K) → j
  12. Segment(B, K) → k
  13. Point({k, RibbeEF, RibbeBE, i, j, g}) → P
  14. Locus(PP, P) → mp1
  15. CircleArc(M, O, J) → p
  16. Segment(O, Q) → l
  17. Segment(Q, A) → m
  18. Line(A, G) → as
  19. Rotate(zijvlakEFGH, α, as) → zijvlakEFGH'
  20. Rotate(E, α, as) → E'
  21. Rotate(B, α, as) → B'
  22. Segment(E', B') → RibbeBE'
  23. Rotate(vierhoek1, α, as) → vierhoek1'
  24. LineBisector(B, B', xOyPlane) → n
  25. Plane(G, n) → q
  26. Mirror(g, q) → g'
  27. Mirror(p, q) → p'
  28. Mirror(J, q) → J'
  29. Mirror(F, q) → F'
  30. Segment(J', F') → i'
  31. Mirror(B, q) → B'_1
  32. Mirror(K, q) → K'
  33. Segment(B'_1, K') → k'
  34. Mirror(Q, q) → Q'
  35. Mirror(A, q) → A'
  36. Segment(Q', A') → m'
  37. Mirror(L, q) → L'
  38. Mirror(K, q) → K'_1
  39. Segment(L', K'_1) → j'
  40. Mirror(O, q) → O'
  41. Mirror(Q, q) → Q'_1
  42. Segment(O', Q'_1) → l'
  43. Mirror(D, q) → D'
  44. Mirror(H, q) → H'
  45. Segment(D', H') → RibbeDH'
  46. Segment(A, D') → r
  47. Segment(B'_1, D') → t
  48. Segment(J, J') → f_1
  49. Segment(F, F') → g_1
  50. Polygon(F, F', G) → driehoek1, g_2, f_2, f'
  51. Polygon(J, J', F', F) → vierhoek2, j_1, h_1, i_1, f_3
  52. Point(g) → S