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SAS Exercise 2: Triangle Transformation

SAS Exercise 2: Triangle Transformation
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2015-12-11 20:46
TriangleTransformationGeometric Construction
In collections CCSS High School: Geometry (Congruence) Volume 1
This example demonstrates triangle transformations in SAS Exercise 2. Key mathematical concepts include geometric transformations, reflection, rotation, and translation. Using GeoGebra commands such as Segment, Angle, Line, Polygon, Mirror, Rotate, etc., the transformed triangle can be constructed. Suitable for middle school and above students to learn geometric transformations.

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

AI Drawing Prompt Reference

Draw triangle ABC, then mirror it to get triangle A'B'C'. Rotate triangle A'B'C' around line d1 to get triangle A''B''C''. Finally, use rotation and mirroring to construct several new segments and triangles, forming a figure with specific angle relationships.
The prompt above was compiled from the original drawing commands and is for reference only.