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Ambiguity of SSA

Ambiguity of SSA
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2015-11-01 15:04
TriangleAngleGeometric Construction
This example demonstrates the ambiguity of constructing a triangle given two sides and a non-included angle (SSA). Key mathematical concepts include triangle solution and geometric construction. It uses commands like Point, Rotate, Angle, Intersect, Polygon, Segment, Ray, If. Suitable for high school geometry.

GeoGebra Commands & Parameters

  1. Point(Semicircle[(x(H) - 4, y(H)), (x(H) + 4, y(H))]) → J
  2. Rotate(A, 330*°, B) → A'
  3. Angle(A', B, A) → α
  4. Intersect(Circle[A, 6], Line[B, A']) → C_1, C
  5. Polygon(A, B, C) → poly1, c, a, b
  6. Point(Ray[D, (x(D) + 1, y(D))]) → E
  7. Segment(D, E) → d
  8. Point(Ray[F, (x(F) + 1, y(F))]) → G
  9. Segment(F, G) → e
  10. Angle(J, H, I) → β
  11. Rotate(P, -γ, Q) → P'
  12. Angle(P', Q, P) → δ
  13. Point(Circle[P, d]) → R
  14. Rotate(I, -γ, H) → I'
  15. Angle(I', H, I) → ε
  16. Segment(I, H) → g
  17. Segment(J, H) → h
  18. Ray(Q, P') → i
  19. Intersect(OrthogonalLine[R, i], i) → K
  20. Polygon(P, Q, R) → poly2, r, p, q
  21. If(Distance[R, K] < 0.01, true, false) → on