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Triangle Congruence Exploration by Marcinek, Tibor

Triangle Congruence Exploration by Marcinek, Tibor
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2016-02-10 03:51
TriangleTransformationGeometric Construction
In collections Triangle Congruence
This GeoGebra applet allows students to explore and discover theorems of triangle congruence, including the uncommon SSA theorem. By adjusting sliders, students can observe and validate the congruence of triangles under different conditions. The applet uses GeoGebra commands such as text field, rotate, angle, ray, point, segment, etc. Suitable for middle school and above students to deepen their understanding of triangle congruence.

GeoGebra Commands & Parameters

  1. Textfield(p) → InputBox1
  2. Textfield(q) → InputBox2
  3. Textfield(α) → InputBox3
  4. Textfield(r) → InputBox4
  5. Textfield(β) → InputBox5
  6. Rotate(A, α, B) → A'
  7. Angle(A, B, A') → δ
  8. Ray(B, A') → a
  9. Point(a) → C
  10. Segment(B, C) → b
  11. Segment(B, A) → c
  12. Textfield(α) → InputBox3_1
  13. Rotate(A_1, α, B_1) → A'_1
  14. Angle(A_1, B_1, A'_1) → δ_1
  15. Ray(B_1, A'_1) → a_1
  16. Point(a_1) → C_1
  17. Segment(B_1, C_1) → b_1
  18. Segment(B_1, A_1) → c_1
  19. Point(Circle[D, p]) → E
  20. Segment(D, E) → d
  21. Textfield(p) → InputBox1_1
  22. Point(Circle[D_1, p]) → E_1
  23. Segment(D_1, E_1) → d_1
  24. Point(Circle[F, q]) → G
  25. Segment(F, G) → e
  26. Textfield(q_1) → InputBox2_1
  27. Point(Circle[F_1, q]) → G_1
  28. Segment(F_1, G_1) → e_1
  29. Point(Circle[H, r]) → I
  30. Segment(H, I) → f
  31. Textfield(r_1) → InputBox4_1
  32. Point(Circle[H_1, r]) → I_1
  33. Segment(H_1, I_1) → f_1
  34. Rotate(J, β, K) → J'
  35. Angle(J, K, J') → ε
  36. Segment(K, J) → g
  37. Ray(K, J') → h
  38. Point(h) → L
  39. Segment(K, L) → i
  40. Textfield(β) → InputBox5_1
  41. Rotate(J_1, β, K_1) → J'_1
  42. Angle(J_1, K_1, J'_1) → ε_1
  43. Segment(K_1, J_1) → g_1
  44. Ray(K_1, J'_1) → h_1
  45. Point(h_1) → L_1
  46. Segment(K_1, L_1) → i_1
  47. Textfield(β) → InputBox5_2
  48. Rotate(J_2, γ, K_2) → J'_2
  49. Angle(J_2, K_2, J'_2) → ε_2
  50. Segment(K_2, J_2) → g_2
  51. Ray(K_2, J'_2) → h_2
  52. Point(h_2) → L_2
  53. Segment(K_2, L_2) → i_2
  54. Textfield(β) → InputBox5_3
  55. Textfield(α) → InputBox3_2
  56. Textfield(β) → InputBox5_4
  57. Textfield(α) → InputBox3_3
  58. Textfield(β) → InputBox5_5
  59. Textfield(β) → InputBox5_6
  60. Rotate(J_3, γ_1, K_3) → J'_3
  61. Angle(J_3, K_3, J'_3) → ε_3
  62. Segment(K_3, J_3) → g_3
  63. Ray(K_3, J'_3) → h_3
  64. Point(h_3) → L_3
  65. Segment(K_3, L_3) → i_3
  66. Textfield(β) → InputBox5_7

AI Drawing Prompt Reference

Draw two triangles ABC and A'B'C', where A and A' are rotated around point B by angle α to get A', and B and C form segment b, while B and A form segment c. Then draw triangle A_1B_1C_1, where A_1 and A'_1 are rotated around point B_1 by angle α to get A'_1, and B_1 and C_1 form segment b_1, while B_1 and A_1 form segment c_1. Next, draw circles with centers D and D_1 and radii p and p_1, and find intersection points E and E_1, then connect DE and D_1E_1. Then draw circles with centers F and F_1 and radii q and q_1, and find intersection points G and G_1, then connect FG and F_1G_1. Finally, draw circles with centers H and H_1 and radii r and r_1, and find intersection points I and I_1, then connect HI and H_1I_1.
The prompt above was compiled from the original drawing commands and is for reference only.