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Parallel Lines and Angles Demo

Parallel Lines and Angles Demo
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2014-11-03 22:48
AngleTransformationGeometric Construction
In collections PARCC Math I Unit 5 Lesson 5
This example demonstrates the relationship between parallel lines and angles, showing dynamically how corresponding and alternate interior angles are equal. It involves core math concepts like parallel line properties, angle measurement, and geometric transformations. Constructed using GeoGebra commands such as Point, Polygon, Segment, Line, Angle, Rotate, Intersect, and TableText to build parallel lines, angles, and transformation relationships. Suitable for high school mathematics teaching to understand parallel line properties and angle relationships.

GeoGebra Commands & Parameters

  1. Point(xAxis) → F
  2. Polygon((x(F), y(Corner[1])), Corner[2], Corner[3], (x(F), y(Corner[4]))) → poly1, c, d, e, f
  3. Segment(G, H) → g
  4. Point(g) → I
  5. Line(A, M) → a
  6. Line(N, D) → b
  7. Line(M, D) → h
  8. Line(A, N) → i
  9. Segment(A, M) → j
  10. Segment(N, D) → k
  11. Segment(M, D) → m
  12. Segment(A, N) → l
  13. Point(i) → E
  14. Angle(M, A, E) → α
  15. Angle(A, M, D) → β
  16. Angle(M, D, N) → γ
  17. Rotate(A, ε, M) → A'
  18. Angle(A, M, A') → ζ
  19. Rotate(D, (-ε), M) → D'
  20. Angle(D', M, D) → η
  21. Angle(A', M, D') → θ
  22. Rotate(D, 345*°, M) → D'_1
  23. Angle(D'_1, M, D) → ι
  24. Angle(D', M, D'_1) → κ
  25. Rotate(M, 9*°, A) → C'
  26. Angle(M, A, C') → λ
  27. Angle(C', A, E) → μ
  28. Rotate(C', ξ, A) → C''
  29. Angle(C', A, C'') → ο
  30. Rotate(C'', ξ, A) → C'''
  31. Angle(C'', A, C''') → ρ
  32. Rotate(C''', ξ, A) → J
  33. Angle(C''', A, J) → σ
  34. Rotate(J, ξ, A) → J'
  35. Angle(J, A, J') → τ
  36. Rotate(M, 55*°, D) → C'_1
  37. Angle(M, D, C'_1) → υ
  38. Angle(C'_1, D, N) → ϕ
  39. Rotate(C'_1, χ, D) → K
  40. Angle(C'_1, D, K) → ψ
  41. Angle(K, D, N) → ω
  42. Intersect(j, l) → L
  43. Line(G, H) → n
  44. Intersect(n, j) → O
  45. Point(l) → B
  46. Line(O, B) → p
  47. Line(B, D) → q
  48. Point(h) → C
  49. Line(D, C) → r
  50. Intersect(j, l) → P
  51. Line(M, P) → s
  52. Intersect(j, l) → Q
  53. Line(Q, N) → t
  54. TableText({{"\mathit{m}\angle 1 + \mathit{m} \angle 2", "=", 180}, {"3(\mathit{x}+15)+2\mathit{x}+55", "=", 180}, {"\mathit{x}", "=", 16}}, "rcl") → text3
  55. TableText({{"\angle 1", "\cong", "\angle 3"}, {"\mathit{m} \angle 1", "=", "\mathit{m} \angle 3"}}, "rcl") → text15
  56. TableText({{"\mathit{m} \angle 3", "=", "4 \mathit{y} + 9"}, {93, "=", "4\mathit{y} + 9"}, {21, "=", "\mathit{y}"}}, "rcl") → text16
  57. TableText({{"\angle 1", "\cong", "\angle 3"}, {"\mathit{m} \angle 1", "=", "\mathit{m} \angle 3"}, {β, "=", α}}, "rcl") → text17