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SAS: Exercise 1

SAS: Exercise 1
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2015-12-08 22:22
TriangleAngleTransformationGeometric Construction
This example demonstrates the geometric construction of triangle congruence using SAS (Side-Angle-Side) postulate. Key math concepts include triangle congruence criteria, angle measurement, segment replication, and geometric transformations. GeoGebra commands like Segment, Angle, Line, Polygon, Mirror, and Rotate are utilized along with objects such as A, B, c, C, b, α, a, etc. Suitable for middle school geometry lessons or student exploration of triangle congruence properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → c
  2. Segment(A, C) → b
  3. Angle(B, A, C) → α
  4. Segment(C, B) → a
  5. Line(D_1, E_1) → d_1
  6. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  7. Mirror(A, d_1) → A'
  8. Mirror(B, d_1) → B'
  9. Mirror(C, d_1) → C'
  10. Polygon(A', B', C') → poly1', c', a', b'
  11. Mirror(A, d_1) → A'_1
  12. Mirror(C, d_1) → F_2
  13. Segment(A'_1, F_2) → e_1
  14. Mirror(A, d_1) → D_2
  15. Mirror(B, d_1) → B'_1
  16. Segment(D_2, B'_1) → f_1
  17. Mirror(C, d_1) → C'_2
  18. Mirror(B, d_1) → E_2
  19. Segment(C'_2, E_2) → d_2
  20. Angle(F_2, D_2, E_2) → β
  21. Rotate(A', 72.13°, F_1) → A''
  22. Rotate(B', 72.13°, F_1) → B''
  23. Rotate(C', 72.13°, F_1) → C''
  24. Polygon(A'', B'', C'') → poly1'', c'', a'', b''
  25. Rotate(A', 72.13°, F_1) → A''_1
  26. Rotate(B', 72.13°, F_1) → B''_1
  27. Rotate(C', 72.13°, F_1) → C''_1
  28. Polygon(A''_1, B''_1, C''_1) → poly1''_1, c''_1, a''_1, b''_1
  29. Rotate(D_2, 72.13°, F_1) → D'
  30. Rotate(B'_1, 72.13°, F_1) → E
  31. Segment(D', E) → f
  32. Rotate(A'_1, 72.13°, F_1) → D
  33. Rotate(F_2, 72.13°, F_1) → F'
  34. Segment(D, F') → e
  35. Rotate(C'_2, 72.13°, F_1) → F
  36. Rotate(E_2, 72.13°, F_1) → E'
  37. Segment(F, E') → d
  38. Angle(F, D, E) → γ