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SSA Congruence Ambiguity Demonstration

SSA Congruence Ambiguity Demonstration
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2016-02-22 11:13
TriangleAngleTrigonometryGeometric Construction
This example demonstrates the invalidity of SSA (Side-Side-Angle) in triangle congruence, highlighting the ambiguous case. It involves core math concepts like triangle congruence criteria, geometric construction, and trigonometry. Constructed using GeoGebra commands such as Ray, Segment, Point, Angle, Rotate, Circle, Intersect, it analyzes the uncertainty of SSA through rotation and intersection analysis. Suitable for high school mathematics teaching to understand the limitations of triangle congruence theorems.

GeoGebra Commands & Parameters

  1. Ray(A, C) → a
  2. Segment(A, B) → b
  3. Point(Circle[D, abs(b)]) → E
  4. Segment(D, E) → c
  5. Angle(C, A, B) → α
  6. Rotate(E, (-α), D) → E'
  7. Angle(E', D, E) → β
  8. Ray(D, E') → d
  9. Point(a) → F
  10. Circle(B, F) → e
  11. Segment(B, F) → f
  12. Circle(E, f) → g
  13. Intersect(g, d, 2) → G
  14. Segment(E, G) → h

AI Drawing Prompt Reference

Draw two triangles sharing a side and an adjacent angle, but positioned differently to show the ambiguity of SSA triangle congruence. One intersection point should be on the extended line of the shared side, while the other is inside it, using circles and ray intersections to analyze the construction uncertainty.
The prompt above was compiled from the original drawing commands and is for reference only.