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ASA Triangle Congruence

ASA Triangle Congruence
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2019-04-09 02:42
TriangleAngleVectorGeometric Construction
In collections Triangle Congruence
This example demonstrates constructing congruent triangles using two angles and the included side. The key mathematical concept is the ASA (Angle-Side-Angle) congruence criterion. Using GeoGebra commands such as Circle, Ray, Rotate, Intersect, Angle, Vector, and Segment, students can understand the construction process of triangle congruence. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, 2) → k
  2. Circle(A, 0.8) → c
  3. Point(c) → B_1
  4. Ray(A, B_1) → l
  5. Rotate(B_1, 30°, A) → B'
  6. Ray(A, B') → i
  7. Intersect(k, i, 1) → B
  8. Angle(B_1, A, B') → α
  9. Circle(C_1, 0.8) → d
  10. Point(d) → D
  11. Rotate(D, 30°, C_1) → D'
  12. Angle(D, C_1, D') → β
  13. Vector(C_1, D') → w
  14. Vector(C_1, D) → a
  15. Circle(E, 2) → e
  16. Point(e) → F
  17. Segment(E, F) → f
  18. Segment(A, B) → j
  19. Circle(A, b) → p
  20. Intersect(p, l, 1) → C
  21. Segment(A, C) → n
  22. Segment(C, B) → m
  23. Angle(A, B, C) → γ
  24. Circle(G, 0.8) → g
  25. Point(g) → H
  26. Vector(G, H) → u
  27. Rotate(H, γ, G) → H'
  28. Angle(H, G, H') → δ
  29. Vector(G, H') → v
  30. Circle(E, 0.8) → h
  31. Circle(F, 0.8) → q
  32. Intersect(h, f, 1) → I
  33. Intersect(q, f, 1) → K_1
  34. Rotate(K_1, (-γ), F) → K
  35. Angle(K, F, K_1) → ε
  36. Rotate(K_1, (-α), F) → M
  37. Angle(M, F, K_1) → ζ
  38. Ray(E, D') → r
  39. Ray(F, H) → s
  40. Intersect(r, s) → L
  41. Segment(E, L) → t
  42. Segment(F, L) → f_1
  43. Ray(G, H') → g_1
  44. Ray(F, D) → h_1
  45. Intersect(g_1, h_1) → N
  46. Segment(G, N) → i_1
  47. Segment(F, N) → j_1

AI Drawing Prompt Reference

Draw a triangle ABC with angles A and B each being 30 degrees and side AB of length 2. First, draw two circles with center A and radii 2 and 0.8, and the intersection point B is on the smaller circle. Then, draw the sides of angles A and B, rotate point B and D, and construct triangle ABC. Next, draw a circle with center C and radius 0.8, and the intersection point D' is on the circle, constructing angle C. Finally, draw triangle DEF with angles D and E each being 30 degrees and side DE of length 2, and construct the corresponding relationship between triangle DEF and triangle ABC.
The prompt above was compiled from the original drawing commands and is for reference only.