MathPlotAI Logo MathPlotAI

Properties of Dilations (Triangle)

Properties of Dilations (Triangle)
Loading the math board and drawing, please wait…
2016-11-13 20:37
TriangleGeometric Construction
This interactive applet demonstrates the properties of triangle dilation as a similarity transformation. It explores how dilations affect the sides and angles of a triangle, emphasizing the concept of scale factor. Students can manipulate the transformation to informally prove why dilations preserve angle measures and proportionality of side lengths. The construction uses commands like Polygon, Segment, Dilate, Circle, Intersect, and Vector. Ideal for middle school and high school students learning about geometric transformations and similarity.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Segment(A, B) → d
  3. Segment(B, C) → e
  4. Segment(C, A) → f
  5. Textfield(k) → InputBox1
  6. Dilate(A, k, O) → A'_5
  7. Dilate(B, k, O) → B'_5
  8. Dilate(C, k, O) → C'
  9. Polygon(A'_5, B'_5, C') → poly1', c', a', b'
  10. Dilate(A, k, O) → A'_1
  11. Dilate(B, k, O) → B'_1
  12. Segment(A'_1, B'_1) → d'
  13. Dilate(B, k, O) → B'_2
  14. Dilate(C, k, O) → C'_1
  15. Segment(B'_2, C'_1) → e'
  16. Dilate(C, k, O) → C'_2
  17. Dilate(A, k, O) → A'_2
  18. Segment(C'_2, A'_2) → f'
  19. Segment(O, A'_5) → g
  20. Segment(O, A) → h
  21. Segment(O, B) → i
  22. Segment(O, B'_5) → j
  23. Segment(O, C') → l
  24. Segment(O, C) → m
  25. Circle(A, 1) → p
  26. Circle(B, 1) → s
  27. Intersect(p, f, 1) → D
  28. Intersect(p, d, 1) → E
  29. Intersect(s, d, 1) → F
  30. Intersect(s, e, 1) → G
  31. CircleSector(A, D, E) → t
  32. CircleSector(B, F, G) → c_1
  33. Dilate(A, If[0 < n ≤ 1, 1 - n, 0], A'_5) → A'_3
  34. Dilate(B, If[1 < n ≤ 2, 2 - n, 0], B'_5) → B'_3
  35. Vector(B, B'_3) → u
  36. Vector(A, A'_3) → v
  37. Translate(t, v) → t'
  38. Translate(c_1, u) → d_1
  39. Angle(D, A, E) → α
  40. CircleSector(A, E, D) → e_1
  41. CircleSector(B, G, F) → f_1
  42. Translate(e_1, v) → g_1
  43. Translate(f_1, u) → h_1
  44. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], A'_5) → A'_4
  45. Vector(A, A'_4) → w
  46. Dilate(B, If[2 < o ≤ 3, 3 - o, 0], B'_5) → B'_4
  47. Vector(B, B'_4) → q
  48. Translate(e_1, w) → r
  49. Rotate(r, If[1 < o ≤ 2, (((o - 1) * 180))°, 180°], A'_5) → r'
  50. Translate(f_1, q) → k_1
  51. Rotate(k_1, If[3 < o ≤ 4, (((o - 3) * 180))°, 180°], B'_5) → p_1
  52. Translate(t, w) → t'_1
  53. Rotate(t'_1, If[1 < o ≤ 2, (((o - 1) * 180))°, 180°], A'_5) → q_1
  54. Translate(c_1, q) → r_1
  55. Rotate(r_1, If[3 < o ≤ 4, (((o - 3) * 180))°, 180°], B'_5) → s_1
  56. Intersect(c', a') → B'
  57. Intersect(c', b') → A'
  58. Intersect(a', b') → J

AI Drawing Prompt Reference

Draw a triangle and demonstrate its dilation transformation. Start by drawing an original triangle, then dilate it from a center point with a scale factor to create a new triangle. Connect the center point to the vertices of both the original and dilated triangles with line segments. Finally, use circles and sectors to indicate angles and show the relationships between the angles and side lengths before and after dilation to prove it's a similarity transformation.
The prompt above was compiled from the original drawing commands and is for reference only.