MathPlotAI Logo MathPlotAI

Exploring ASA and AAS for Triangle Congruence

Exploring ASA and AAS for Triangle Congruence
Loading the math board and drawing, please wait…
2014-03-07 03:37
TriangleAngleTransformation
In collections Unit 4 Triangle Congruence Theorems
This example uses GeoGebra to explore triangle congruence under the ASA (two angles and included side) and AAS (two angles and a non-included side) conditions. Key mathematical concepts include the conditions for triangle congruence. Using commands like Point, Segment, Polygon, Angle, Rotate, Ray, Intersect, Vector, Translate, students can visually understand these conditions. Suitable for middle school and above students learning geometry.

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