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Triangle Dilation Demo

Triangle Dilation Demo
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2017-11-13 06:44
TriangleTransformationGeometric Construction
This example demonstrates the transformation of a triangle under dilation, involving core concepts like dilation transformation, similar triangles, and distance calculations. It uses commands such as Polygon, Dilate, Ray, and Distance in GeoGebra. Suitable for high school geometry and transformation studies.

GeoGebra Commands & Parameters

  1. Polygon(B, C, D) → poly1, d, b, c
  2. Dilate(B, a, A) → B'
  3. Dilate(C, a, A) → C'
  4. Dilate(D, a, A) → D'
  5. Polygon(B', C', D') → poly1', d', b', c'
  6. Ray(A, D) → e
  7. Ray(A, B) → f
  8. Ray(A, C) → g
  9. Distance(A, D) → distanceAD
  10. Distance(A, D') → distanceAD'
  11. Distance(A, B) → distanceAB
  12. Distance(A, B') → distanceAB'
  13. Distance(A, C) → distanceAC
  14. Distance(A, C') → distanceAC'
  15. Distance(B, C) → distanceBC
  16. Distance(B', C') → distanceB'C'
  17. Distance(D', C') → distanceD'C'
  18. Distance(D, C) → distanceDC
  19. Distance(B, D) → distanceBD
  20. Distance(B', D') → distanceB'D'
  21. Dilate(B_1, a, A_1) → B'_1
  22. Dilate(D_1, a, A_1) → D'_1
  23. Ray(A_1, D_1) → e_1
  24. Ray(A_1, B_1) → f_1
  25. Distance(A_1, D_1) → distanceAD_1
  26. Distance(A_1, D'_1) → distanceAD'_1
  27. Distance(A_1, B_1) → distanceAB_1
  28. Distance(A_1, B'_1) → distanceAB'_1
  29. Distance(B_1, D_1) → distanceBD_1
  30. Distance(B'_1, D'_1) → distanceB'D'_1
  31. Dilate(B_2, a, A_2) → B'_2
  32. Dilate(C_1, a, A_2) → C'_1
  33. Ray(A_2, B_2) → f_2
  34. Ray(A_2, C_1) → g_1
  35. Distance(A_2, B_2) → distanceAB_2
  36. Distance(A_2, B'_2) → distanceAB'_2
  37. Distance(A_2, C_1) → distanceAC_1
  38. Distance(A_2, C'_1) → distanceAC'_1
  39. Distance(B_2, C_1) → distanceBC_1
  40. Distance(B'_2, C'_1) → distanceB'C'_1

AI Drawing Prompt Reference

Draw a triangle ABC, then dilate B, C, and D around point A with scale factor a to get triangle A'B'C'. Draw rays from A to D, B, and C, and measure the lengths of AD, AD', AB, AB', AC, AC', BC, B'C', DC, BD, and B'D'. Finally, dilate B1 and D1 around point A' with scale factor a to get B'_1 and D'_1, and draw rays from A' to D1 and B1, and measure the lengths of A'D1, A'B1, A'B1, A'B'_1, A'D1, and A'D'_1.
The prompt above was compiled from the original drawing commands and is for reference only.