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Tool for Compositions of Rigid and Similar Transformations

Tool for Compositions of Rigid and Similar Transformations
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2014-09-17 08:14
FunctionCoordinate GeometryTransformation
In collections Congruence (CO) Cluster Congruence (Vol 1) Congruence (Vol 1) Over 80 Resources CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1
This example demonstrates the composition of rigid and similar transformations. Rigid transformations include translation, rotation, and reflection, while similar transformations include these with scaling. By adjusting parameters, observe the effects of the combined transformations. Key mathematical concepts include geometric transformations, similarity transformations, and scaling. GeoGebra commands used include TextField, Segment, Element, Polygon, etc. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Textfield(m) → inputBox1
  2. Textfield(b) → inputBox2
  3. Segment(A, B) → a
  4. Segment(B, C) → c
  5. Segment(C, A) → d
  6. Element(A5, 1, 1) → B5
  7. Element(A5, 1, 2) → C5
  8. Element(A6, 1, 1) → B6
  9. Element(A7, 1, 1) → B7
  10. Element(A6, 1, 2) → C6
  11. Element(A7, 1, 2) → C7
  12. Element(A9, 1, 1) → B9
  13. Element(A9, 1, 2) → C9
  14. Element(A10, 1, 1) → B10
  15. Element(A11, 1, 1) → B11
  16. Element(A10, 1, 2) → C10
  17. Element(A11, 1, 2) → C11
  18. Element(A13, 1, 1) → B13
  19. Element(A14, 1, 1) → B14
  20. Element(A15, 1, 1) → B15
  21. Element(A18, 1, 1) → B18
  22. Element(A18, 1, 2) → C18
  23. Element(A19, 1, 1) → B19
  24. Element(A19, 1, 2) → C19
  25. Element(A20, 1, 1) → B20
  26. Element(A20, 1, 2) → C20
  27. Segment(D15, D14) → g
  28. Segment(D13, D14) → h
  29. Segment(D15, D13) → i
  30. Segment(D20, D19) → j
  31. Segment(D19, D18) → k
  32. Segment(D18, D20) → l
  33. Segment(D11, D9) → n
  34. Segment(D9, D10) → p
  35. Segment(D10, D11) → q
  36. Segment(D6, D7) → r
  37. Segment(D5, D7) → s
  38. Segment(D6, D5) → t
  39. Polygon(D, F, G, E) → poly1, d_1, f_1, g_1, e_1
  40. Polygon(H, I, J, K) → poly2, h_1, i_1, j_1, k_1
  41. Polygon(L, M, N, O) → poly3, l_1, m_1, n_1, o_1
  42. Element(A23, 1, 1) → B23
  43. Element(A23, 1, 2) → C23
  44. Element(A24, 1, 1) → B24
  45. Element(A24, 1, 2) → C24
  46. Element(A25, 1, 1) → B25
  47. Element(A25, 1, 2) → C25
  48. Segment(D23, D25) → a_1
  49. Segment(D24, D25) → b_1
  50. Segment(D24, D23) → c_1
  51. Segment(A28, A30) → q_1
  52. Segment(A30, A29) → r_1
  53. Segment(A29, A28) → s_1
  54. Polygon(P, Q, R, S) → poly4, p_2, q_2, r_2, s_2
  55. Shuffle({0, 0, 0, 0, 0, 0, 3 + 0 * v_1}) → A55
  56. Element(A55, 1) → A56
  57. Shuffle({1, 1, 1, 1, 0.7, 1.2, 0.4, 1.5, 0.3, 1, 1, 1, 1.1, 1.3, 1 + 0 * v_1}) → A59
  58. Element(A59, 1) → A60
  59. Shuffle({0, 0, 0, 0, 0, 0, 0, 1, 2, -1, -2, 1, 1, 4, 0, 0, 0, 0 * v_1}) → A51
  60. Segment(E64, E63) → t_1
  61. Segment(E62, E63) → a_2
  62. Segment(E62, E64) → b_2
  63. Textfield(m) → inputBox3

AI Drawing Prompt Reference

Draw a geometric pattern composed of rigid and similar transformations, showing the effects of different transformation parameters. Start with a base triangle, then generate multiple transformed triangles using input parameters for translation, rotation, reflection, and scaling, and connect these triangles with lines to form a complex pattern.
The prompt above was compiled from the original drawing commands and is for reference only.