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SSA Exploration

SSA Exploration
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2018-09-18 03:06
TriangleTrigonometryGeometric ConstructionSlider AnimationLocus
In collections Triangle Congruence
This example demonstrates the construction of triangles given two side lengths and an included angle, exploring the conditions for unique or multiple solutions under SSA criteria. It involves core mathematical concepts such as triangle construction, geometric principles, and the SSA ambiguity. The construction utilizes commands like Point, Segment, Rotate, Angle, Line, Circle, Intersect, and Polygon in GeoGebra. Suitable for high school mathematics education to understand the uniqueness or variability of triangle solutions under SSA conditions.

GeoGebra Commands & Parameters

  1. Point(Circle[A, abs(AB)]) → B
  2. Segment(A, B) → d
  3. Rotate(B, b, A) → B'
  4. Angle(B, A, B') → α
  5. Line(A, B') → e
  6. Circle(B, BC) → f
  7. Intersect(f, e) → C1, D
  8. Segment(D, B) → g
  9. Segment(C1, B) → h
  10. Segment(A, D) → i
  11. Point(f) → C
  12. Segment(B, C) → j
  13. Segment(C1, C) → k
  14. Segment(D, C) → l
  15. Polygon(A, C1, B) → poly1, b_1, a_1, c1
  16. Angle(poly1) → β, γ, δ
  17. Polygon(A, D, B) → poly2, b_2, a_2, d_2
  18. Angle(poly2) → ε, ζ, η