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Angle-Side-Angle (ASA): Quick Exploration

Angle-Side-Angle (ASA): Quick Exploration
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2023-01-03 22:31
TriangleAngleGeometric Construction
This example demonstrates constructing a triangle using two given angles and the included side, verifying the Angle-Side-Angle congruence theorem. It involves core concepts like triangle congruence, angle measurement, and segment length. Construction uses GeoGebra commands such as Ray, Rotate, Point, Intersect, Segment, and Circle. Suitable for middle school and above students learning geometric constructions and proofs.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Rotate(B, α, A) → B'
  3. Ray(A, B') → g
  4. Point(f) → C
  5. Rotate(A, (-β), C) → A'
  6. Ray(C, A') → h
  7. Intersect(g, h) → D
  8. Segment(A, C) → i
  9. Segment(A, D) → j
  10. Segment(D, C) → k
  11. Min({i, j, k}) → a
  12. Circle(A, (0.35 * a)) → c
  13. Circle(C, (0.35 * a)) → d
  14. Intersect(c, i) → E,
  15. Intersect(c, j, 1) → F
  16. Intersect(d, i, 1) → G
  17. Intersect(d, k, 1) → H
  18. CircleSector(A, E, F) → e
  19. CircleSector(C, H, G) → p
  20. Circle(I, i) → q
  21. Point(q) → J
  22. Segment(I, J) → l
  23. Rotate(J, α, I) → J'
  24. Ray(I, J') → m
  25. Rotate(I, (-β), J) → I'
  26. Ray(J, I') → n
  27. Intersect(m, n) → K
  28. Segment(I, K) → r
  29. Segment(K, J) → s
  30. Line(L, M) → t
  31. Circle(I, (0.35 * a)) → c_1
  32. Circle(J, (0.35 * a)) → d_1
  33. Intersect(c_1, l, 1) → N
  34. Intersect(c_1, r, 1) → O
  35. Intersect(d_1, s) → P,
  36. Intersect(d_1, l, 1) → Q
  37. CircleSector(J, P, Q) → e_1
  38. CircleSector(I, N, O) → f_1
  39. Rotate(J, (-α), I) → J'_{1}
  40. Rotate(I, β, J) → I'_{1}
  41. Ray(I, J'_{1}) → b
  42. Ray(J, I'_{1}) → g_1
  43. Intersect(b, g_1) → R
  44. Polygon(A, C, D) → t1, d_2, a_1, c_2

AI Drawing Prompt Reference

Draw a triangle with two given angles α and β and the included side AC. Start by drawing a ray AB, then rotate point B to get B'. Draw a ray AB', and pick a point C on it. Rotate point A around C by -β to get A', and draw a ray CA'. The intersection of these two rays is point D. Connect AD and CD to form triangle ACD.
The prompt above was compiled from the original drawing commands and is for reference only.