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Exploring the Three Parallels Theorem

Exploring the Three Parallels Theorem
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2019-05-23 02:46
TriangleCoordinate GeometryGeometric Construction
This example uses GeoGebra to explore the three parallels theorem. Key concepts include parallel lines, distance, and triangles. Commands used include Line, Distance, Point, etc. Suitable for middle school and above students to learn geometric proofs and explore properties.

GeoGebra Commands & Parameters

  1. Line(A, B) → a_1
  2. Circle(A, a) → c
  3. OrthogonalLine(A, a_1) → b
  4. Intersect(c, b, 1) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, b) → D, E
  7. OrthogonalLine(E, b) → e
  8. Circle(E, a) → f
  9. Intersect(f, b, 2) → F
  10. OrthogonalLine(F, b) → g
  11. Circle(C, a) → h
  12. Intersect(h, b) → G, H
  13. OrthogonalLine(G, b) → i
  14. Distance(F, E) → distanceFE
  15. Distance(E, A) → distanceEA
  16. Distance(A, C) → distanceAC
  17. Distance(C, G) → distanceCG
  18. Point(b) → I
  19. Point(b) → J
  20. Point(g) → K
  21. Point(i) → L
  22. Line(K, L) → j
  23. Intersect(e, j) → O
  24. Intersect(a_1, j) → P
  25. Intersect(d, j) → Q
  26. Segment(K, O) → k
  27. Segment(O, P) → l
  28. Segment(P, Q) → m
  29. Segment(Q, L) → n
  30. Point(g) → M
  31. Point(i) → N
  32. Segment(M, N) → p
  33. Intersect(e, p) → R
  34. Intersect(a_1, p) → S
  35. Intersect(d, p) → T
  36. Segment(M, R) → q
  37. Segment(R, S) → r
  38. Segment(S, T) → s
  39. Segment(T, N) → t
  40. Circle(N, 3) → c_1
  41. Circle(T, 3) → d_1
  42. Circle(S, 3) → e_1
  43. Circle(R, 3) → f_1
  44. Intersect(f_1, e, 1) → U
  45. Intersect(f_1, q, 1) → V
  46. Intersect(e_1, a_1, 2) → W
  47. Intersect(e_1, r, 1) → Z
  48. Intersect(d_1, d, 1) → A_1
  49. Intersect(d_1, s, 1) → B_1
  50. Intersect(c_1, i, 1) → C_1
  51. Intersect(c_1, t, 1) → D_1
  52. CircleSector(R, U, V) → g_1
  53. CircleSector(S, W, Z) → h_1
  54. CircleSector(T, A_1, B_1) → k_1
  55. CircleSector(N, C_1, D_1) → p_1