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Rhombus Properties Illustrated by Tim Brzezinski

Rhombus Properties Illustrated by Tim Brzezinski
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2016-05-08 06:32
PolygonAngleVectorGeometric 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 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Unit 7: Polygons and Quadrilaterals Quadrilaterals
This example demonstrates the properties of a rhombus without relying on segment lengths or angle measures. Key mathematical concepts include equal sides, perpendicular and bisecting diagonals, and angle bisectors. GeoGebra commands and objects used in construction are Circle, Line, Intersect, CircleArc, Point, Segment, Min, Dilate, Angle, Rotate, CircleSector, Polygon, Vector, and Translate. Suitable for high school geometry education to visually illustrate and understand rhombus properties.

GeoGebra Commands & Parameters

  1. Circle(B, A) → f
  2. Circle(A, B) → c
  3. Line(A, B) → b
  4. Intersect(c, b, 2) → C
  5. CircleArc(A, B, C) → d
  6. Point(d) → D
  7. Segment(D, B) → s
  8. Circle(D, A) → e
  9. Intersect(e, f, 2) → E
  10. Segment(A, E) → n
  11. Intersect(n, s) → L
  12. Segment(A, B) → a
  13. Segment(A, D) → g
  14. Segment(D, E) → h
  15. Segment(E, B) → i
  16. Min(g, h) → j
  17. Dilate(B, If[0 < l ≤ 1, 1 - l, 0], A) → B'
  18. Segment(B, B') → m
  19. Angle(E, B, A) → α
  20. Angle(D, E, B) → β
  21. Rotate(B, If[1 < l ≤ 2, ((-(l - 1)) * α), α], B) → B'_1
  22. Rotate(B', If[1 < l ≤ 2, ((-(l - 1)) * α), (-α)], B) → B''
  23. Segment(B'_1, B'') → m'
  24. Rotate(B'_1, If[2 < l ≤ 3, ((-(l - 2)) * β), (-β)], E) → J
  25. Rotate(B'', If[2 < l ≤ 3, ((-(l - 2)) * β), (-β)], E) → B'''
  26. Segment(J, B''') → m''
  27. Rotate(J, If[3 < l ≤ 4, ((-(l - 3)) * α), (-α)], D) → J'
  28. Rotate(B''', If[3 < l ≤ 4, ((-(l - 3)) * α), (-α)], D) → K
  29. Segment(J', K) → m'''
  30. Circle(B, (0.2 * j)) → k
  31. Circle(E, (0.2 * j)) → p
  32. Intersect(p, m'', 1) → F
  33. Intersect(p, m', 1) → G
  34. Intersect(k, m', 1) → H
  35. Intersect(k, m, 1) → I
  36. CircleSector(B, H, I) → q
  37. CircleSector(E, F, G) → r
  38. Polygon(A, B, E, D) → poly1, a_1, b_1, e_1, d_1
  39. Dilate(B, If[5 < l ≤ 6, 6 - l, 0], D) → B'_2
  40. Vector(B, B'_2) → u
  41. Translate(q, u) → q'
  42. Rotate(q', If[6 < l ≤ 7, ((l - 6) * π), 3.141592653589793], D) → q''
  43. Dilate(E, If[7 < l ≤ 8, 8 - l, 0], A) → E'
  44. Vector(E, E') → v
  45. Translate(r, v) → r'
  46. Rotate(r', If[8 < l ≤ 9, ((-(l - 8)) * π), -3.141592653589793], A) → r''
  47. Dilate(D, If[9 < l ≤ 10, 10 - l, 0], L) → D'
  48. Vector(D, D') → w
  49. Min(n / 2, s / 2) → o
  50. Circle(L, (0.2 * o)) → t
  51. Intersect(t, s, 2) → M
  52. Intersect(t, n, 2) → N
  53. CircleSector(L, M, N) → c_1
  54. Segment(D, D') → f_1
  55. Dilate(L, If[10 < l ≤ 11, 11 - l, 0], B) → L'
  56. Circle(D, (0.2 * j)) → h_1
  57. Intersect(k, s) → P,
  58. Intersect(s, f_1) → Q
  59. Intersect(h_1, s, 1) → O
  60. Circle(A, (0.2 * j)) → k_1
  61. Intersect(k_1, m, 1) → R
  62. Intersect(k_1, n, 1) → S
  63. Intersect(k_1, m''', 1) → T
  64. Intersect(h_1, m'', 1) → U
  65. CircleSector(D, O, U) → q_1
  66. Dilate(A, If[11 < l ≤ 12, 12 - l, 0], L) → A'
  67. Segment(A, A') → i_1
  68. Dilate(L, If[12 < l ≤ 13, 13 - l, 0], E) → L'_1
  69. Segment(L, L'_1) → j_1
  70. Intersect(p, m'', 1) → V
  71. Intersect(p, n, 1) → W
  72. CircleSector(A, S, T) → s_1
  73. CircleSector(B, P, I) → p_1
  74. Intersect(p, m', 1) → Z
  75. CircleSector(E, W, Z) → r_1
  76. Segment(L, L') → g_1
  77. Rotate(L, If[13 < l ≤ 14, ((-(l - 13)) * π), -3.141592653589793], L) → L'_2
  78. Rotate(L', If[13 < l ≤ 14, ((-(l - 13)) * π), -3.141592653589793], L) → L''
  79. Segment(L'_2, L'') → l_1
  80. Rotate(L, If[14 < l ≤ 15, ((-(l - 14)) * π), 3.141592653589793], L) → L'_3
  81. Rotate(L'_1, If[14 < l ≤ 15, ((-(l - 14)) * π), 3.141592653589793], L) → A_1
  82. Segment(L'_3, A_1) → m_1
  83. Rotate(q_1, If[15 < l ≤ 16, ((-(l - 15)) * α / 2), ((-α)) / 2], D) → t_1
  84. Rotate(p_1, If[15 < l ≤ 16, ((-(l - 15)) * α / 2), ((-α)) / 2], B) → c_2
  85. Rotate(s_1, If[16 < l ≤ 17, ((-(l - 16)) * β / 2), ((-β)) / 2], A) → d_2
  86. Rotate(r_1, If[16 < l ≤ 17, ((-(l - 16)) * β / 2), ((-β)) / 2], E) → e_2
  87. Rotate(c_1, If[17 < l ≤ 18, ((l - 17) * π / 2), 1.5707963267948966], L) → f_2

AI Drawing Prompt Reference

Draw a rhombus with four equal sides, two perpendicular and bisecting diagonals, and angle bisectors. Start by drawing two circles to determine the vertices of the rhombus, then connect these vertices to form the rhombus. Next, draw the diagonals, ensuring they are perpendicular and bisect each other. Finally, draw the angle bisectors, making sure they intersect the diagonals.
The prompt above was compiled from the original drawing commands and is for reference only.