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Triangle Congruence Criteria by David

Triangle Congruence Criteria by David
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2015-07-16 07:22
TriangleGeometric Construction
This example demonstrates the criteria for triangle congruence. It involves key mathematical concepts such as triangle congruence and logic. Using GeoGebra commands like Point, Segment, Polygon, etc., it constructs triangles that meet the congruence criteria. Suitable for middle school and above students to learn about geometric construction and the concept of congruent triangles.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 3]) → B
  2. Segment(A, B) → a
  3. Point(Circle[C, 5]) → D
  4. Segment(C, D) → b
  5. Point(Circle[E, 7]) → F
  6. Segment(E, F) → c
  7. Polygon(G, H, 4) → poly1, d, e, f, g, I, J
  8. Distance(H, d) → distanceHd
  9. Point(Circle[K, 18]) → L
  10. Segment(K, L) → h
  11. Polygon(K, L, 4) → poly2, i, j, k, l, M, N
  12. Point(Circle[O, 4]) → P
  13. Segment(O, P) → m
  14. Point(Circle[Q, 6]) → R
  15. Segment(Q, R) → n
  16. Rotate(S, 50*°, T) → S'
  17. Angle(S, T, S') → α
  18. Segment(T, S) → p
  19. Segment(T, S') → q
  20. Point(Circle[U, 18]) → V
  21. Segment(U, V) → r
  22. Polygon(U, V, 4) → poly3, s, t, a_1, b_1, W, Z
  23. Rotate(A_1, -50*°, B_1) → C_1
  24. Angle(C_1, B_1, A_1) → β
  25. Segment(A_1, B_1) → c_1
  26. Segment(C_1, B_1) → d_1
  27. Point(Circle[D_1, 6]) → E_1
  28. Segment(D_1, E_1) → e_1
  29. Rotate(F_1, 30*°, G_1) → H_1
  30. Angle(F_1, G_1, H_1) → γ
  31. Segment(H_1, G_1) → f_1
  32. Segment(G_1, F_1) → g_1
  33. Point(Circle[I_1, 18]) → J_1
  34. Segment(I_1, J_1) → h_1
  35. Polygon(I_1, J_1, 4) → poly4, i_1, j_1, k_1, l_1, K_1, L_1
  36. Rotate(M_1, 30*°, N_1) → O_1
  37. Angle(M_1, N_1, O_1) → δ
  38. Segment(N_1, M_1) → m_1
  39. Segment(O_1, N_1) → n_1
  40. Rotate(P_1, -70*°, Q_1) → R_1
  41. Angle(R_1, Q_1, P_1) → ε
  42. Segment(P_1, Q_1) → p_1
  43. Segment(Q_1, R_1) → q_1
  44. Point(Circle[S_1, 18]) → T_1
  45. Segment(S_1, T_1) → r_1
  46. Polygon(S_1, T_1, 4) → poly5, s_1, t_1, a_2, b_2, U_1, V_1
  47. Point(Circle[W_1, 7]) → Z_1
  48. Segment(W_1, Z_1) → c_2
  49. Point(Circle[A_2, 8]) → B_2
  50. Segment(A_2, B_2) → d_2
  51. Rotate(C_2, -50*°, D_2) → E_2
  52. Angle(E_2, D_2, C_2) → ζ
  53. Segment(D_2, C_2) → e_2
  54. Segment(D_2, E_2) → f_2
  55. Rotate(F_2, 80*°, G_2) → H_2
  56. Angle(F_2, G_2, H_2) → η
  57. Segment(H_2, G_2) → g_2
  58. Segment(G_2, F_2) → h_2

AI Drawing Prompt Reference

Draw a set of diagrams illustrating triangle congruence criteria. Start with three base segments of lengths 3, 5, and 7 units. Then construct a quadrilateral and measure the distance from one side to the opposite side. Next, draw a segment of length 18 units and construct another quadrilateral. Create an angle of 50 degrees with its two sides. Then draw another 18-unit segment, construct a third quadrilateral, and create a 50-degree angle with its sides. After that, draw a 6-unit segment, construct a 30-degree angle with its sides, then draw an 18-unit segment, construct a fourth quadrilateral, and create a 30-degree angle. Finally, draw an 18-unit segment, construct a fifth quadrilateral, create a 70-degree angle, and draw a 7-unit segment. The overall figure demonstrates various side-length and angle combinations for triangle congruence.
The prompt above was compiled from the original drawing commands and is for reference only.