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30-60-90 Special Right Triangle Discovery Learning Resource

30-60-90 Special Right Triangle Discovery Learning Resource
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2016-04-27 20:28
TriangleCircleGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Triangle Theorems Special Right Triangles Special Right Triangles
This example demonstrates the properties and construction of a 30-60-90 special right triangle. Key math concepts include right triangles, special angles, side length ratios, and similarity. Construction highlights involve using GeoGebra commands such as Polygon, Dilate, Segment, Circle, Intersect, CircleSector, Rotate, Vector, Translate, Midpoint, and Ray. Suitable for high school students to explore geometric properties and applications of special right triangles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], B) → A'
  3. Segment(A, A') → e
  4. Dilate(B, If[1 < d ≤ 2, 2 - d, 0], C) → B'
  5. Dilate(C, If[2 < d ≤ 3, 3 - d, 0], A) → C'
  6. Segment(A, B) → h
  7. Segment(A, C) → i
  8. Segment(B, C) → j
  9. Circle(A, (0.15 * h)) → k
  10. Intersect(k, i, 1) → D
  11. Intersect(k, h, 1) → E
  12. CircleSector(A, E, D) → p
  13. Rotate(A, If[3.5 < d ≤ 4.5, ((d - 3.5) * π / 3), 1.0471975511965976], A) → A'_1
  14. Rotate(A', If[3.5 < d ≤ 4.5, ((d - 3.5) * π / 3), 1.0471975511965976], A) → A''
  15. Segment(A'_1, A'') → e'
  16. Rotate(A, If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * π / 3), -1.0471975511965976], B) → A'_2
  17. Rotate(A', If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * π / 3), -1.0471975511965976], B) → A''_1
  18. Segment(A'_2, A''_1) → e'_1
  19. Dilate(A, If[6 < d ≤ 7, 7 - d, 0], B) → A'_3
  20. Vector(A, A'_3) → u
  21. Translate(p, u) → p'
  22. Rotate(p', If[7 < d ≤ 8, (((d - 7) * 2) * π / 3), 2.0943951023931953], B) → p''
  23. Circle(B, (0.15 * h)) → r
  24. Intersect(r, j, 1) → F
  25. Intersect(r, h, 1) → K
  26. Dilate(B, If[8 < d ≤ 9, 9 - d, 0], C) → B'_1
  27. Vector(B, B'_1) → v
  28. Translate(p'', v) → p'''
  29. Rotate(p''', If[9 < d ≤ 10, (((d - 9) * 2) * π / 3), 2.0943951023931953], C) → t
  30. Circle(C, (0.15 * h)) → c_1
  31. Intersect(c_1, i) → M,
  32. Intersect(c_1, j) → N,
  33. Midpoint(h) → O
  34. Dilate(C, If[10 < d ≤ 11, 11 - d, 0], O) → C'_1
  35. Segment(C, C'_1) → l
  36. Circle(O, (0.15 * h)) → d_1
  37. Segment(C, O) → m
  38. Intersect(d_1, m, 1) → P
  39. Intersect(d_1, h) → Q, R
  40. Polygon(A, O, C) → poly2, c_2, a_1, o
  41. Intersect(c_1, m) → S,
  42. CircleSector(C, S, N) → e_1
  43. CircleSector(O, R, P) → f_1
  44. Segment(O, B) → n
  45. Rotate(e_1, If[13 < d ≤ 14, ((-(d - 13)) * π / 6), -0.5236], C) → h_1
  46. Rotate(O, If[13.25 < d ≤ 14.25, ((-(d - 13.25)) * π), -3.141592653589793], O) → O'
  47. Rotate(B, If[14 < d ≤ 15, ((d - 14) * π), 3.14159], O) → B'_2
  48. Segment(O', B'_2) → n'
  49. Segment(O, B) → b_1
  50. Dilate(C, If[15 < d ≤ 16, 16 - d, 0], A) → C'_2
  51. Vector(C, C'_2) → w
  52. Translate(h_1, w) → q_1
  53. Dilate(C, If[17 < d ≤ 18, 18 - d, 0], A) → C'_3
  54. Vector(C, C'_3) → u_1
  55. Translate(h_1, u_1) → s_1
  56. Rotate(O', If[19 < d ≤ 20, ((d - 19) * π / 3), 1.0472], A) → O''
  57. Rotate(B'_2, If[18.25 < d ≤ 19.25, ((d - 18.25) * π / 3), 1.0471975511965976], A) → U
  58. Segment(O'', U) → n''
  59. Rotate(O'', If[19.25 < d ≤ 20.25, ((d - 19.25) * π), π], O'') → O'''
  60. Rotate(U, If[20 < d ≤ 21, ((d - 20) * π), π], O'') → U'
  61. Segment(O''', U') → n'''
  62. Rotate(f_1, If[12 < d ≤ 13, ((d - 12) * π / 2), 1.5708], O) → g_1
  63. Rotate(q_1, If[16 < d ≤ 17, (((-(d - 16)) * 4) * π / 3), -4.18879], A) → r_1
  64. Rotate(s_1, If[18 < d ≤ 19, (((-(d - 18)) * 7) * π / 6), -3.66519], A) → t_1
  65. Rotate(E, π / 6, A) → E'
  66. Ray(A, E') → f
  67. Circle(A, (0.2 * h)) → q
  68. Intersect(q, f, 1) → G
  69. Segment(A, G) → g

AI Drawing Prompt Reference

Draw a 30-60-90 special right triangle to demonstrate its side length ratios and angle relationships. Start by constructing an equilateral triangle, then shorten and scale one side to form a right triangle. Next, draw a circle centered at the right angle vertex, intersecting the hypotenuse and one leg to locate the 30° and 60° angles. Use rotations and dilations to create additional shapes like circular sectors and similar triangles, resulting in a comprehensive geometric illustration with labeled elements.
The prompt above was compiled from the original drawing commands and is for reference only.