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Triangle Congruence Exploration by rikeylee

Triangle Congruence Exploration by rikeylee
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2013-01-22 02:57
TriangleAngleGeometric ConstructionSlider Animation
In collections Triangle congruence
This example demonstrates the conditions for triangle congruence through interactive manipulation. It involves core math concepts like triangle congruence criteria (SSS, SAS, ASA, AAS), relationships between angles and sides. Construction uses GeoGebra commands/objects such as Point, Polygon, Segment, Intersect, Angle. Suitable for middle school and above students to understand geometric proofs and explore properties.

GeoGebra Commands & Parameters

  1. Point(Circle[A_{SS}, AB]) → B_{SS}
  2. Point(Circle[B_{SS}, BC]) → C_{SS}
  3. Polygon(A_{SS}, B_{SS}, C_{SS}) → tri_{SS}, c_{ss}, a_{ss}, b_{ss}
  4. Point(Circle[A_{SA}, AB]) → B_{SA}
  5. Point(Ray[Rotate[B_{SA}, (-angB), B_{SA}], Rotate[A_{SA}, angB, B_{SA}]]) → C_{SA}
  6. Polygon(A_{SA}, B_{SA}, C_{SA}) → tri_{SA}, c_{sa}, a_{sa}, b_{sa}
  7. Point(Circle[A_{SSS}, AB]) → B_{SSS}
  8. Point(Circle[B_{SSS}, BC]) → C_{SSS}
  9. Point(Circle[C_{SSS}, CA]) → AC_{SSS}
  10. Segment(A_{SSS}, B_{SSS}) → a
  11. Segment(B_{SSS}, C_{SSS}) → b
  12. Segment(C_{SSS}, AC_{SSS}) → c
  13. Polygon(A_{SSS}, B_{SSS}, C_{SSS}) → tri_{SSS}, c_{sss}, a_{sss}, b_{sss}
  14. Point(Circle[A_{SSA}, AB]) → B_{SSA}
  15. Point(Circle[B_{SSA}, BC]) → C_{SSA}
  16. Point(Ray[Rotate[C_{SSA}, (-angC), C_{SSA}], Rotate[B_{SSA}, angC, C_{SSA}]]) → AC_{SSA}
  17. Polygon(A_{SSA}, B_{SSA}, C_{SSA}) → tri_{SSA}, c_{ssa}, a_{ssa}, b_{ssa}
  18. Point(Circle[A_{AAS}, CA]) → C_{AAS}
  19. Point(Ray[Rotate[A_{AAS}, angA, A_{AAS}], Rotate[C_{AAS}, angA, A_{AAS}]]) → BA_{AAS}
  20. Intersect(Ray[Rotate[A_{AAA}, (-angA), A_{AAA}], Rotate[B_{AAA}, (-angA), A_{AAA}]], Ray[Rotate[B_{AAA}, angB, B_{AAA}], Rotate[A_{AAA}, angB, B_{AAA}]]) → C_{AAA}
  21. Polygon(A_{AAA}, B_{AAA}, C_{AAA}) → tri_{AAA}, c_{aaa}, a_{aaa}, b_{aaa}
  22. Angle(A_{SA}, B_{SA}, C_{SA}) → α
  23. Segment(A_{SSA}, B_{SSA}) → d
  24. Segment(B_{SSA}, C_{SSA}) → e
  25. Segment(C_{SSA}, AC_{SSA}) → f
  26. Angle(B_{SSA}, C_{SSA}, AC_{SSA}) → β
  27. Segment(A_{AAS}, C_{AAS}) → g
  28. Segment(A_{AAS}, BA_{AAS}) → h
  29. Angle(C_{AAS}, A_{AAS}, BA_{AAS}) → γ
  30. Point(Circle[A_{ASA}, CA]) → C_{ASA}
  31. Segment(A_{ASA}, C_{ASA}) → m
  32. Point(Ray[Rotate[A_{ASA}, angA, A_{ASA}], Rotate[C_{ASA}, angA, A_{ASA}]]) → BA_{ASA}
  33. Segment(A_{ASA}, BA_{ASA}) → n
  34. Point(Ray[Rotate[C_{ASA}, (-angC), C_{ASA}], Rotate[A_{ASA}, (-angC), C_{ASA}]]) → BC_{ASA}
  35. Segment(C_{ASA}, BC_{ASA}) → p
  36. Intersect(Ray[A_{ASA}, BA_{ASA}], Ray[C_{ASA}, BC_{ASA}]) → B_{ASA}
  37. Polygon(A_{ASA}, B_{ASA}, C_{ASA}) → tri_{ASA}, c_{asa}, a_{asa}, b_{asa}
  38. Angle(BA_{ASA}, A_{ASA}, C_{ASA}) → ζ
  39. Angle(BC_{ASA}, C_{ASA}, A_{ASA}) → η
  40. Angle(C_{AAA}, B_{AAA}, A_{AAA}) → θ
  41. Angle(B_{AAA}, A_{AAA}, C_{AAA}) → ι
  42. Angle(A_{AAA}, C_{AAA}, B_{AAA}) → κ
  43. Point(Ray[Rotate[BA_{AAS}, angB, BA_{AAS}], Rotate[A_{AAS}, angB, BA_{AAS}]]) → CB_{AAS}
  44. Segment(BA_{AAS}, CB_{AAS}) → i
  45. Angle(CB_{AAS}, BA_{AAS}, A_{AAS}) → δ
  46. Intersect(Ray[Rotate[C_{AAS}, (-angC), C_{AAS}], Rotate[A_{AAS}, (-angC), C_{AAS}]], Ray[Rotate[A_{AAS}, angA, A_{AAS}], Rotate[C_{AAS}, angA, A_{AAS}]]) → B_{AAS}
  47. Polygon(A_{AAS}, B_{AAS}, C_{AAS}) → tri_{AAS}, c_{aas}, a_{aas}, b_{aas}
  48. Point(Circle[A_{SAS}, AB]) → B_{SAS}
  49. Intersect(Circle[A_{SAS}, CA], Ray[Rotate[A_{SAS}, (-angA), A_{SAS}], Rotate[B_{SAS}, (-angA), A_{SAS}]]) → C_{SAS},
  50. Polygon(A_{SAS}, B_{SAS}, C_{SAS}) → tri_{SAS}, c_{sas}, a_{sas}, b_{sas}
  51. Angle(C_{SAS}, A_{SAS}, B_{SAS}) → ε

AI Drawing Prompt Reference

Draw three triangles to demonstrate the criteria for triangle congruence: SSS, SAS, ASA, and AAS. Each triangle should be colored differently, with its three sides and angles labeled. Include sliders to control the angles. Start with a triangle showing SSS congruence, then add one for SAS, followed by ASA, and finally AAS. Label each triangle with its congruence criterion and angle measures. Use the sliders to adjust the angles and observe how the congruence conditions change.
The prompt above was compiled from the original drawing commands and is for reference only.