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H2M 2019 P1 Q12

H2M 2019 P1 Q12
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2020-06-25 20:44
TriangleVectorSolid Geometry
This example demonstrates a problem involving similar triangles in 3D vectors. Key mathematical concepts include vectors, similar triangles, and percentages. It constructs 3D vectors, similar triangles, and percentage calculations to help students understand geometric transformations in 3D space. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Random(1, 2) → px
  2. Random(2, 3) → py
  3. Random(4, 5) → pz
  4. Random(-1, -2) → ux
  5. Random(-3, -4) → uy
  6. Random(-5, -6) → uz
  7. Line(P, u) → f
  8. Random(-4, -5) → sx
  9. Random(-5, -6) → sy
  10. Random(-6, -7) → sz
  11. Line(S, u) → g
  12. Random(1, 2) → a4
  13. Random(1, 1) → a2
  14. Random(1, 1) → a1
  15. Random(1, 1) → a3
  16. Intersect(p, f) → Q
  17. FractionText(Q) → textQ
  18. Random(-7, -11) → b4
  19. Intersect(q, g) → R
  20. FractionText(R) → textR
  21. OrthogonalLine(Q, p) → h
  22. OrthogonalLine(R, q) → i
  23. Segment(Q, R) → j
  24. Vector(P, Q) → vPQ
  25. Vector(R, S) → vRS
  26. Vector(Q, R) → vQR
  27. Point(h) → A
  28. Angle(A, Q, P) → θ
  29. Point(h) → B
  30. Angle(R, Q, B) → β
  31. Intersect(q, h) → C
  32. Segment(Q, C) → k
  33. SurdText(cosα) → textcα
  34. SurdText(cosβ) → textcβ
  35. SurdText(k) → textDist
  36. Plane(P, Q, R) → r
  37. SurdText(D) → textD
  38. FractionText(d2) → text3
  39. Numerator(d2) → d3
  40. Denominator(d2) → d4
  41. SurdText(d5) → text4
  42. Point(h) → E
  43. Point(h) → F
  44. Segment(E, F) → l
  45. PointIn(p) → G
  46. PointIn(p) → H
  47. PointIn(p) → I
  48. Line(G, H) → m
  49. Mirror(I, m) → I'
  50. Line(I, I') → n
  51. Intersect(m, n) → J
  52. Line(G, n) → s
  53. Line(I, m) → t
  54. Intersect(t, s) → K
  55. Polygon(I, J, G, K) → q1, i_1, j_1, g_1, k_1
  56. Prism(q1, (-k)) → b, L, edgeIL, edgeJM, edgeGN, edgeKO, edgeLM, edgeMN, edgeNO, edgeLO, M, N, O, faceIJML, faceGJMN, faceGKON, faceIKOL, faceLMNO