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ASA Congruence Postulate Demo

ASA Congruence Postulate Demo
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2016-10-03 08:49
TriangleAngleGeometric Construction
In collections Chapter 4 - Triangle Congruence - Geometry
This example demonstrates the Angle-Side-Angle (ASA) Congruence Postulate in triangles, proving two triangles are congruent when two angles and the included side are equal. It involves core concepts like triangle congruence criteria, angle measurement, and side length calculation. Construction highlights include using GeoGebra commands such as Vector, Segment, Angle, Circle, Point, Intersect, and Line. Suitable for middle school and above students to understand geometric proofs and constructions.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(A, C) → v
  3. Vector(D, E) → w
  4. Vector(D, F) → a
  5. Segment(G, H) → f
  6. Angle(C, A, B) → α
  7. Circle(I, Segment[G, H]) → c
  8. Point(c) → J
  9. Segment(I, J) → g
  10. Circle(I, Segment[A, C]) → d
  11. Circle(I, Segment[A, B]) → e
  12. Intersect(d, g, 1) → K
  13. Circle(K, Segment[C, B]) → h
  14. Intersect(e, h, 1) → L
  15. Segment(I, L) → i
  16. Circle(J, Segment[F, D]) → k
  17. Circle(J, Segment[D, E]) → p
  18. Intersect(k, g, 1) → M
  19. Circle(M, Segment[F, E]) → q
  20. Line(I, L) → j
  21. Intersect(p, q, 2) → N
  22. Line(J, N) → l
  23. Angle(E, D, F) → β
  24. Intersect(j, l) → O
  25. Angle(O, J, I) → γ
  26. Angle(J, I, O) → δ
  27. Segment(J, O) → m
  28. Segment(O, I) → n
  29. Circle(P, Segment[G, H]) → r
  30. Point(r) → Q
  31. Segment(P, Q) → s
  32. Circle(P, Segment[A, C]) → t
  33. Circle(P, Segment[A, B]) → c_1
  34. Intersect(t, s, 1) → R
  35. Circle(R, Segment[C, B]) → d_1
  36. Intersect(c_1, d_1, 1) → S
  37. Line(P, S) → b
  38. Circle(Q, Segment[D, F]) → e_1
  39. Circle(Q, Segment[D, E]) → f_1
  40. Intersect(e_1, s, 1) → T
  41. Circle(T, Segment[F, E]) → g_1
  42. Intersect(f_1, g_1, 2) → U
  43. Line(Q, U) → h_1
  44. Intersect(b, h_1) → V
  45. Segment(V, P) → i_1
  46. Segment(V, Q) → j_1
  47. Angle(V, Q, P) → ε
  48. Angle(Q, P, V) → ζ

AI Drawing Prompt Reference

Draw two triangles to demonstrate the Angle-Side-Angle (ASA) Congruence Postulate. First, construct a triangle with two specified angles and the included side, then create a second triangle with corresponding equal angles and side. Use circles and intersection points to locate the vertices, label all angles and sides, and connect the vertices with line segments to complete the congruent triangle construction.
The prompt above was compiled from the original drawing commands and is for reference only.