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Angle Between Lateral Faces of a Rectangular Pyramid

Angle Between Lateral Faces of a Rectangular Pyramid
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2018-03-10 10:55
AngleTrigonometrySolid GeometryGeometric Construction
This GeoGebra example dynamically illustrates the dihedral angle between the lateral faces of a rectangular pyramid, adjusting in real time as the base edge ratios change. Core mathematical concepts include solid geometry, dihedral angles, trigonometric relationships, and proportional reasoning in three-dimensional space. Construction utilizes GeoGebra commands such as Point, Polygon, Midpoint, Segment, Sequence, Sphere, IntersectConic, Angle, Rotate, OrthogonalPlane, Intersect, and conditional If statements, involving vertices A, B, C, D and associated midpoints, diagonals, and face objects. The model is suitable for high school geometry, trigonometry, and early college solid geometry courses, helping learners visualize how lateral face angles respond to base dimension variations.

GeoGebra Commands & Parameters

  1. Point(Sequence[A + (i, 0, 0), i, 1, 100]) → B
  2. Point(Sequence[B + (0, i, 0), i, 1, 100]) → C
  3. Polygon(A, B, C, D) → q1, a, b, c, d
  4. Midpoint(A, C) → O
  5. Segment(O, B) → m
  6. Segment(G_1, B) → n
  7. Sequence(A + (a / 2, b / 2, sqrt(i^(2) - m^(2))), i, n, n + 100) → L_1
  8. Point(L_1) → V
  9. Sphere(A, 18) → e
  10. Sphere(B, 18) → f
  11. IntersectConic(e, f) → g
  12. Sphere(C, 18) → h
  13. Angle(V, Midpoint[B, C], O) → α
  14. Rotate(A, (t * (180° - α)), b) → A'
  15. Rotate(V, (t * (180° - α)), b) → V'
  16. Polygon(V', A', B) → t1, b_1, v', a'
  17. Polygon(V', B, C) → t2, c_1, v'_1, b_2
  18. Point(c_1) → F
  19. OrthogonalPlane(F, c_1) → i
  20. Intersect(v', i) → F_1
  21. Intersect(b_1, i) → G_2
  22. Intersect(b, i) → H
  23. Intersect(b_2, i) → I
  24. If(Defined[F_1], F_1, G_2) → E
  25. If(Defined[H], H, I) → G
  26. Segment(F, E) → j
  27. Segment(F, G) → k
  28. Polygon({V, C, D}) → t3
  29. Polygon({V, A, D}) → t4
  30. Segment(V, D) → l
  31. Angle(E, F, G) → β
  32. Angle(V', F, E) → γ
  33. Angle(G, F, V') → δ