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Is SSA Congruent?

Is SSA Congruent?
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2019-06-25 04:40
TriangleAngleGeometric Construction
This example explores whether a triangle is uniquely determined by two sides and the included angle (SSA). Key mathematical concepts include triangle congruence, angle concepts, and geometric construction. Using GeoGebra commands such as Circle, Point, Segment, etc., it dynamically demonstrates different scenarios of triangle construction. Suitable for middle school and above students or teachers to understand the conditions for triangle congruence.

GeoGebra Commands & Parameters

  1. Circle(B, B_1) → c
  2. Point(c) → A
  3. Point(c) → D
  4. Segment(B, A) → a
  5. Segment(B, D) → b
  6. Segment(D, A) → d
  7. Ray(A, D) → e
  8. Point(e) → E_1
  9. Ray(D, E_1) → f
  10. Point(f) → C
  11. Segment(B, C) → g
  12. Segment(D, C) → h
  13. Vector((0, 0), (0, -3)) → u
  14. Translate(B, u) → F
  15. Translate(A, u) → E
  16. Segment(F, E) → a'
  17. Translate(B, u) → A'_1
  18. Translate(D, u) → H
  19. Segment(A'_1, H) → b'
  20. Translate(D, u) → D'_1
  21. Translate(A, u) → C'_1
  22. Segment(D'_1, C'_1) → d'
  23. Translate(B, u) → A'_2
  24. Translate(C, u) → G
  25. Segment(A'_2, G) → g'
  26. Translate(D, u) → H_1
  27. Translate(C, u) → F'_1
  28. Segment(H_1, F'_1) → h'
  29. Segment(E, G) → i
  30. Segment(A, C) → j
  31. Angle(B, C, A) → α
  32. Angle(F, G, H) → β
  33. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  34. Polygon(F, G, H) → poly2, h_1, f_1, g_1