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Angle Relationships Multi‑Step Problem (7.G.2.5)

Angle Relationships Multi‑Step Problem (7.G.2.5)
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2016-01-13 12:43
AngleVectorTransformationGeometric Construction
① This example demonstrates how to apply supplementary, complementary, vertical, and adjacent angle properties to set up and solve equations for unknown angles in a multi‑step configuration of intersecting lines and rays. ② Core math concepts: angle classification and relationships, linear equation formulation and solving, multi‑step geometric reasoning. ③ Construction highlights: GeoGebra commands Intersect, Line, OrthogonalLine, Point, AngularBisector, Rotate, Angle, Ray, Vector create points A, B, C…, rays, vectors, and angle labels α, β, γ, δ, ε; text objects display each algebraic step. ④ Suitable for middle‑school geometry (Grade 7) lessons on angle relationships, classroom presentation, and student inquiry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Line(A, B) → a
  3. OrthogonalLine(A, a) → b
  4. Point(a) → C
  5. Point(b) → D
  6. Point(b) → E
  7. AngularBisector(C, A, D) → c
  8. Point(c) → F
  9. Rotate(B, 18*°, A) → B'
  10. Angle(B, A, B') → α
  11. Line(B', A) → d
  12. AngularBisector(B', A, D) → e
  13. Point(e) → G
  14. Ray(A, G) → f
  15. Point(d) → H
  16. Rotate(H, 24*°, A) → H'
  17. Angle(H, A, H') → β
  18. Ray(A, H') → g
  19. Rotate(H', 24*°, A) → H''
  20. Angle(H', A, H'') → γ
  21. Ray(A, H'') → h
  22. Rotate(E, 15*°, A) → E'
  23. Angle(E, A, E') → δ
  24. Ray(A, E') → i
  25. Angle(E, A, B) → ε
  26. Point(a) → J
  27. Point(d) → K
  28. Point(c) → L
  29. Vector(A, D) → u
  30. Vector(A, G) → v
  31. Vector(A, K) → w
  32. Vector(A, J) → j
  33. Vector(A, L) → k
  34. Vector(A, E') → l
  35. Vector(A, E) → m
  36. Vector(A, H'') → n
  37. Vector(A, H') → p
  38. Vector(A, H) → q
  39. Vector(A, C) → r
  40. Vector(A, F) → s
  41. Angle(F, A, C) → ζ
  42. Angle(L, A, J) → η
  43. Angle(D, A, F) → θ
  44. Angle(E, A, L) → ι
  45. Angle(D, A, C) → κ
  46. Vector(A, K) → u_1
  47. Vector(A, G) → v_1
  48. Vector(A, D) → w_1
  49. Vector(A, F) → e_1
  50. Vector(A, C) → f_1
  51. Vector(A, H) → g_1
  52. Vector(A, H') → h_1
  53. Vector(A, H'') → i_1
  54. Vector(A, E) → j_1
  55. Vector(A, E') → k_1
  56. Vector(A, L) → l_1
  57. Vector(A, J) → m_1