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Angles between planes (concept check)

Angles between planes (concept check)
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2020-05-01 19:30
VectorSolid GeometryGeometric Construction
This example demonstrates the calculation and visualization of the angle between two planes. Key math concepts include plane equations, vector dot product, and angle computation. GeoGebra commands like Point, Polygon, Circle, Intersect, Segment, Vector, OrthogonalPlane, Translate, and Angle are used to construct planes and vectors, with vector dot product and magnitude calculations to find the angle. Suitable for high school solid geometry teaching or self-study to understand spatial geometric relationships.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, D) → poly1, d, a, b
  4. Polygon(A, C, B) → poly2, b_1, a_1, c
  5. Circle(A, 6, zAxis) → e
  6. Circle(B, 6, zAxis) → f
  7. Circle(A, 6, xAxis) → g
  8. Circle(B, 6, xAxis) → h
  9. Intersect(e, g) → E, F, ,
  10. Intersect(f, h) → G, H, ,
  11. Segment(F, H) → i
  12. Point(i) → I
  13. Vector(F, I) → u
  14. Point(c) → J
  15. OrthogonalPlane(J, c) → j
  16. Intersect(b_1, j) → K
  17. Intersect(b, j) → L
  18. Segment(K, J) → k
  19. Segment(J, L) → l
  20. Polygon(A, J, L) → poly3, l_1, a_2, j_1
  21. Polygon(A, J, K) → poly4, k_1, a_3, j_2
  22. Polygon(J, K, C, B) → poly5, j_3, k_2, c_1, b_2
  23. Polygon(J, L, D, B) → poly6, j_4, l_2, d_1, b_3
  24. Intersect(a_1, j) → M
  25. Intersect(a, j) → N
  26. Segment(M, J) → m
  27. Segment(J, N) → n
  28. Polygon(C, M, J, A) → poly7, c_2, m_1, j_5, a_4
  29. Polygon(M, B, J) → poly8, j_6, m_2, b_4
  30. Polygon(A, J, N, D) → poly9, a_5, j_7, n_1, d_2
  31. Polygon(N, J, B) → poly10, b_5, n_2, j_8
  32. Translate(poly5, u) → poly5'
  33. Translate(poly6, u) → poly6'
  34. Translate(poly8, u) → poly8'
  35. Translate(poly10, u) → poly10'
  36. Angle(D, A, C) → α
  37. Angle(K, J, L) → β
  38. Angle(C, B, D) → γ
  39. Angle(K, J, A) → δ
  40. Angle(L, J, A) → ε
  41. Angle(M, J, N) → ζ
  42. Angle(M, J, A) → η
  43. Angle(N, J, A) → θ
  44. Angle(M, J, L) → ι
  45. Angle(K, J, N) → κ
  46. Segment(K, J) → s