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Congruence of Triangles by Rigid Motions

Congruence of Triangles by Rigid Motions
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2014-06-08 11:40
TriangleVectorTransformation
In collections Transformations Stations
This example demonstrates the congruence of triangles by applying a series of transformations to move one triangle onto another. Key mathematical concepts include the conditions for triangle congruence and rigid motions. It utilizes commands such as Polygon, Line, Vector, Translate, Circle, Point, Angle, Mirror, Rotate, and Segment in GeoGebra. Suitable for middle school and above students to learn about geometric transformations and triangle congruence.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Line(E, D) → d
  3. Vector(F, G) → v
  4. Translate(A, v) → A'_1
  5. Translate(B, v) → B'_1
  6. Translate(C, v) → C'_1
  7. Polygon(A'_1, B'_1, C'_1) → Translation, c'_1, a'_1, b'_1
  8. Circle(H, I) → e
  9. Point(e) → J
  10. Angle(I, H, J) → α
  11. Mirror(A'_1, d) → L
  12. Mirror(B'_1, d) → M
  13. Mirror(C'_1, d) → N
  14. Polygon(L, M, N) → TransRef, n, l, m
  15. Rotate(L, α, K) → L'
  16. Rotate(M, α, K) → M'
  17. Rotate(N, α, K) → N'
  18. Polygon(L', M', N') → TransRefRot, n', l', m'
  19. Segment(J, H) → f
  20. Segment(I, H) → g
  21. Mirror(A, d) → A'
  22. Mirror(B, d) → B'
  23. Mirror(C, d) → C'
  24. Polygon(A', B', C') → Reflection, c', a', b'
  25. Rotate(A, α, K) → A'_2
  26. Rotate(B, α, K) → B'_2
  27. Rotate(C, α, K) → C'_2
  28. Polygon(A'_2, B'_2, C'_2) → Rotation, c'_2, a'_2, b'_2
  29. Rotate(A'_1, α, K) → O
  30. Rotate(B'_1, α, K) → P
  31. Rotate(C'_1, α, K) → Q
  32. Polygon(O, P, Q) → TransRot, q, o_1, p
  33. Mirror(A'_2, d) → R
  34. Mirror(B'_2, d) → S
  35. Mirror(C'_2, d) → T
  36. Polygon(R, S, T) → RefRot, t, r_1, s
  37. Line(V, W) → f_1
  38. Vector((0, 0), (g_1, h_1)) → u_1
  39. Translate(A, u_1) → A'_3
  40. Translate(B, u_1) → B'_3
  41. Translate(C, u_1) → C'_3
  42. Polygon(A'_3, B'_3, C'_3) → poly1', c'_3, a'_3, b'_3
  43. Rotate(A, β, U) → A'_4
  44. Rotate(B, β, U) → B'_4
  45. Rotate(C, β, U) → C'_4
  46. Polygon(A'_4, B'_4, C'_4) → poly1'_1, c'_4, a'_4, b'_4
  47. Mirror(A, f_1) → A'_5
  48. Mirror(B, f_1) → B'_5
  49. Mirror(C, f_1) → C'_5
  50. Polygon(A'_5, B'_5, C'_5) → poly1'_2, c'_5, a'_5, b'_5
  51. Rotate(A'_3, β, U) → Z
  52. Rotate(B'_3, β, U) → A_1
  53. Rotate(C'_3, β, U) → B_1
  54. Polygon(Z, A_1, B_1) → poly1'', b_2, z_1, a_2
  55. Mirror(A'_3, f_1) → C_1
  56. Mirror(B'_3, f_1) → D_1
  57. Mirror(C'_3, f_1) → E_1
  58. Polygon(C_1, D_1, E_1) → poly1''_1, e_2, c_2, d_2
  59. Mirror(A'_4, f_1) → F_1
  60. Mirror(B'_4, f_1) → G_1
  61. Mirror(C'_4, f_1) → H_1
  62. Polygon(F_1, G_1, H_1) → poly2, h_2, f_2, g_2
  63. Mirror(Z, f_1) → Z'
  64. Mirror(A_1, f_1) → I_1
  65. Mirror(B_1, f_1) → J_1
  66. Polygon(Z', I_1, J_1) → poly1''', j_1, z', i_1

AI Drawing Prompt Reference

Draw two congruent triangles to demonstrate their relationship through translation, rotation, and reflection. Start by drawing a triangle, then translate it to a new position. Show how to obtain another congruent triangle by rotating and reflecting the first one. Finally, combine these transformations to verify the congruence of the triangles.
The prompt above was compiled from the original drawing commands and is for reference only.