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SSA Congruence

SSA Congruence
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2015-12-01 00:44
TriangleAngleGeometric Construction
This example demonstrates the congruence of triangles under the SSA (two sides and a non-included angle) condition. Key mathematical concepts include the conditions for triangle congruence. Using GeoGebra commands such as Polygon, Circle, Point, Segment, Intersect, Ray, and Angle, the construction of triangles satisfying the SSA condition is illustrated. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Circle(A', c) → d
  3. Point(d) → B'
  4. Segment(A', B') → e
  5. Circle(B', a) → f
  6. Point(b) → F
  7. Circle(C, F) → g
  8. Intersect(g, a, 1) → G
  9. Circle(F, G) → h
  10. Point(f) → C'
  11. Segment(B', C') → i
  12. Circle(C', Radius[g]) → k
  13. Intersect(k, i, 1) → I
  14. Circle(I, Radius[h]) → p
  15. Intersect(k, p, 1) → J
  16. Ray(C', J) → j
  17. Angle(B, C, A) → α
  18. Angle(B', C', J) → β

AI Drawing Prompt Reference

Draw a triangle ABC where AB=AC and the side opposite to angle A (BC) is known, but the side opposite to angle B (AC) is unknown. First, draw line segments AB and AC, then draw a circle with center A and radius BC, and another circle with center C and radius AB, their intersection is point C'. Connect BC', then draw a circle with center C' and radius C'I, and their intersection with BC is point I. Connect CI, finally draw the side AC opposite to angle B, resulting in triangle ABC.
The prompt above was compiled from the original drawing commands and is for reference only.