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ASA and AAS Triangle Congruence

ASA and AAS Triangle Congruence
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2019-02-06 07:50
TriangleAngleGeometric Construction
In collections Triangle Congruence Criteria Visual Representations
This example demonstrates how to prove triangle congruence using Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) criteria. It involves core mathematical concepts such as triangle congruence theorems, geometric constructions, and angle measurements. The construction utilizes GeoGebra commands/objects like Point, Segment, Polygon, Angle, Rotate, Ray, Intersect, Vector, and Translate. Suitable for high school students learning triangle congruence criteria.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 10]) → B
  2. Segment(A, B) → a
  3. Polygon(A, B, C) → poly1, c, a_1, b
  4. Angle(A, B, C) → α
  5. Angle(C, A, B) → β
  6. Point(Circle[D, 10]) → E
  7. Segment(D, E) → d
  8. Rotate(E, (-β), D) → E'
  9. Angle(E', D, E) → γ
  10. Rotate(D, α, E) → D'
  11. Angle(D, E, D') → δ
  12. Ray(E, D') → e
  13. Ray(D, E') → f
  14. Intersect(e, f) → F
  15. Segment(D, F) → g
  16. Segment(F, E) → h
  17. Angle(B, C, A) → ε
  18. Angle(E, F, D) → ζ
  19. Angle(B, C, A) → η
  20. Angle(A, B, C) → ι
  21. Vector(B, E) → u
  22. Translate(A, u) → A'
  23. Translate(B, u) → B'
  24. Translate(A, u) → A'_1
  25. Translate(B, u) → B'_1
  26. Segment(A'_1, B'_1) → a'_1
  27. Vector(G, H) → v
  28. Vector(I, J) → w
  29. Translate(A, w) → A'_2
  30. Translate(B, w) → B'_2
  31. Translate(C, w) → C'
  32. Polygon(A'_2, B'_2, C') → poly1', c', a'_2, b'_2
  33. Translate(A, w) → A'_3
  34. Translate(B, w) → B'_3
  35. Segment(A'_3, B'_3) → a'
  36. Translate(G, w) → G'
  37. Translate(A, v) → A'_4
  38. Translate(B, v) → B'_4
  39. Translate(C, v) → C'_1
  40. Polygon(A'_4, B'_4, C'_1) → poly1'_1, c'_1, a'_4, b'_4
  41. Translate(A, v) → A'_5
  42. Translate(B, v) → B'_5
  43. Segment(A'_5, B'_5) → a'_3
  44. Angle(B'_4, A'_4, C'_1) → θ
  45. Angle(C'_1, B'_4, A'_4) → κ
  46. Angle(B'_4, C'_1, A'_4) → λ
  47. Ray(E, F) → i
  48. Ray(D, F) → j
  49. Ray(A'_4, C'_1) → k
  50. Ray(C'_1, B'_4) → l