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A Plane in a Cube

A Plane in a Cube
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2016-08-23 12:04
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates a plane within a cube. It involves key concepts in solid geometry. Using GeoGebra commands such as Point, Cube, Intersect, etc., the construction of the cube and its faces and edges is shown. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Point(Circle[A, Distance[B, A], Segment[B, A]]) → C
  2. Cube(B, A, C) → a, D, faceCDHG, faceEFGH, edgeBD, edgeAB, edgeAC, edgeCD, edgeBE, edgeDH, edgeEH, edgeEF, E, edgeAF, edgeFG, edgeCG, edgeGH, F, G, H, faceABDC, faceBDHE, faceABEF, faceACGF
  3. Intersect(edgeCG, g) → O
  4. Intersect(edgeAC, g) → P
  5. Intersect(edgeAB, g) → Q
  6. Intersect(edgeBE, g) → R
  7. Intersect(edgeEH, g) → S
  8. Intersect(edgeGH, g) → T
  9. Intersect(edgeFG, g) → V
  10. Intersect(edgeEF, g) → W
  11. Intersect(edgeAF, g) → Z
  12. Intersect(edgeCD, g) → A_1
  13. Intersect(edgeDH, g) → B_1
  14. Intersect(edgeBD, g) → C_1
  15. Line(D, F) → i
  16. IntersectPath(g, a) → poly1, I, m, n, p, J, K, L, M, N, j, k, l
  17. Angle(poly1, poly1) → α, β, γ, δ, ε, ζ
  18. Angle(Intersect[i, g] + Vector[(1, -1, 1)], Intersect[i, g], Intersect[i, g] + Vector[(1, 1, 0)]) → η
  19. Circle(M, N, O) → c
  20. Circle(A_1, B_1, C_1) → d
  21. Circle(V, W, Z) → e
  22. Segment(F, Intersect[i, g]) → q
  23. Segment(Intersect[i, g], D) → r