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Exploring SSA for Triangle Congruence

Exploring SSA for Triangle Congruence
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2017-10-23 06:30
TriangleTrigonometryGeometric Construction
In collections D.G. 4.4 & 4.5: Triangle Congruence Shortcuts
This GeoGebra applet dynamically demonstrates why SSA (two sides and an angle) is not a valid criterion for triangle congruence. It involves constructing triangles using polygons, circles, angles, and line segments. Suitable for middle school and above students to learn about triangle congruence criteria.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Point(b) → G
  3. Point(a) → H
  4. Angle(A, B, C) → γ
  5. Angle(B, C, A) → δ
  6. Angle(C, A, B) → ε
  7. Circle(B', Segment[A, B]) → d
  8. Point(d) → A'
  9. Circle(B', Segment[C, B]) → e
  10. Point(e) → C'
  11. Segment(B', C') → f
  12. Segment(B', A') → g
  13. Intersect(d, f, 1) → I
  14. CircleArc(B', A', I) → h
  15. Circle(C', Segment[H, C]) → k
  16. Circle(C', Segment[G, C]) → p
  17. Intersect(k, f, 1) → D
  18. Circle(D, Segment[H, G]) → q
  19. Intersect(p, q, 1) → E
  20. Ray(C', E) → i
  21. Point(i) → F
  22. Segment(F, C') → j
  23. Angle(A', B', C') → β
  24. Angle(B', C', F) → ζ
  25. Angle(C', F, B') → η

AI Drawing Prompt Reference

Draw a triangle ABC with AB and AC of the same length but different angle BAC. Try to construct another triangle using the SSA condition and observe the result. First, draw triangle ABC, then draw a circle with center B and radius AB, and another circle with center C and radius AC, let their intersection be D, connect BD and CD, then draw a circle with center D and radius DH, intersecting the previous circle at E, connect CE and EF, and finally get triangle BDE, observe its relationship with triangle ABC.
The prompt above was compiled from the original drawing commands and is for reference only.