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Dynamic HL Theorem Illustration

Dynamic HL Theorem Illustration
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2017-03-26 11:49
TriangleCircleGeometric Construction
In collections Triangle Congruence
This example dynamically demonstrates the HL Theorem for congruent right triangles, visually showing that right triangles with equal hypotenuses and one leg are congruent. Key math concepts include the HL Theorem, congruence criteria for right triangles, and geometric construction. Construction highlights involve using commands like Line, Segment, Circle, Intersect, Rotate, Angle, Point, Polygon, Dilate, and objects such as Vector and Translation in GeoGebra. Suitable for high school mathematics education to help students intuitively understand the application and proof of the HL Theorem.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Segment(A, B) → g
  3. OrthogonalLine(B, g) → h
  4. Circle(B, 1) → c
  5. Intersect(c, h, 2) → C
  6. Ray(B, C) → i
  7. Rotate(B, (a * pi / 180), A) → B'
  8. Angle(B, A, B') → α
  9. Ray(A, B') → j
  10. Intersect(h, j) → D
  11. Segment(A, D) → k
  12. Segment(D, B) → l
  13. Angle(D, B, A) → β
  14. Circle(E, g) → d
  15. Point(d) → F
  16. Segment(E, F) → m
  17. OrthogonalLine(F, m) → n
  18. Circle(F, l) → e
  19. Intersect(e, n, 2) → G
  20. Segment(F, G) → p
  21. Segment(G, E) → q
  22. Polygon(A, B, D) → poly1, d_1, a_1, b
  23. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'
  24. Segment(A, A') → r
  25. Dilate(D, If[1 < o ≤ 2, 2 - o, 0], B) → D'
  26. Segment(D, D') → s
  27. Line(A, q) → t
  28. Point(t) → H
  29. Angle(D, A, H) → γ
  30. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], G) → D'_1
  31. Vector(D, D'_1) → u
  32. Translate(A, u) → A'_1
  33. Translate(A', u) → A''
  34. Segment(A'_1, A'') → r'
  35. Rotate(A'_1, If[3 < o ≤ 4, ((o - 3) * γ), γ], A'') → I
  36. Rotate(A'', If[3 < o ≤ 4, ((o - 3) * γ), γ], A'') → A'''
  37. Segment(I, A''') → r''
  38. Line(D, p) → f_1
  39. Point(f_1) → J
  40. Angle(B, D, J) → δ
  41. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], G) → D'_2
  42. Vector(D, D'_2) → v
  43. Translate(D, v) → D'_3
  44. Translate(D', v) → D''
  45. Segment(D'_3, D'') → s'
  46. Rotate(D'_3, If[4 < o ≤ 5, ((o - 4) * δ), δ], D'_3) → K
  47. Rotate(D'', If[4 < o ≤ 5, ((o - 4) * δ), δ], D'_3) → D'''
  48. Segment(K, D''') → s''
  49. Segment(E, F) → g_1
  50. Angle(G, F, E) → ε
  51. Dilate(D, If[6 < o ≤ 7, 7 - o, 0], G) → D'_4
  52. Vector(D, D'_4) → w
  53. Translate(A, w) → A'_2
  54. Translate(B, w) → B'_1
  55. Translate(D, w) → D'_5
  56. Polygon(A'_2, B'_1, D'_5) → poly1', d'_5, a'_2, b'_1
  57. Rotate(A'_2, If[7 < o ≤ 8, ((o - 7) * γ), γ], G) → L
  58. Rotate(B'_1, If[7 < o ≤ 8, ((o - 7) * γ), γ], G) → M
  59. Rotate(D'_5, If[7 < o ≤ 8, ((o - 7) * γ), γ], G) → N
  60. Polygon(L, M, N) → poly1'', n_1, l_1, m_1
  61. Segment(A, B) → h_1