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Isosceles Trapezoid Template (Scaffolded Discovery) by Tim Brzezinski

Isosceles Trapezoid Template (Scaffolded Discovery) by Tim Brzezinski
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2016-10-12 02:54
PolygonTransformationGeometric 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 construction of an isosceles trapezoid. Key mathematical concepts include geometric transformations, similarity transformations, and polygons. Using GeoGebra commands such as line, ray, point, midpoint, slope, orthogonal line, mirror, dilate, segment, circle, intersect, vector, translate, angle, rotate, polygon, and distance, students can explore the properties of an isosceles trapezoid. Suitable for middle and high school students for geometric exploration and learning.

GeoGebra Commands & Parameters

  1. Line(A, B_1) → a
  2. Ray(A, B_1) → b
  3. Point(b) → B
  4. Midpoint(A, B) → D_1
  5. Line(A, B) → c
  6. Slope(c) → d
  7. OrthogonalLine(D_1, c) → g
  8. Point(g) → E_1
  9. Ray(D_1, E_1) → h
  10. Point(h) → F
  11. Slope(h) → i
  12. Line(F, c) → l
  13. Point(l) → G
  14. Point(l) → H
  15. Ray(F, G) → m
  16. Ray(F, H) → n
  17. Point(m) → D
  18. Mirror(D, h) → I'
  19. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  20. Segment(A, A') → p
  21. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_1
  22. Segment(A, A'_1) → q
  23. Segment(A, B) → r
  24. Segment(B, I') → s
  25. Segment(I', D) → t
  26. Segment(D, A) → a_1
  27. Circle(A, (0.2 * Min[a_1, r])) → c_1
  28. Circle(D, (0.2 * Min[a_1, r])) → d_1
  29. Intersect(d_1, a_1, 1) → J
  30. Intersect(d_1, t, 1) → K
  31. Intersect(c_1, r, 1) → L
  32. Intersect(c_1, a_1, 1) → M
  33. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], I') → I'_1
  34. Segment(D, I'_1) → b_1
  35. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], B) → A'_2
  36. Vector(A, A'_2) → u
  37. Translate(A, u) → A'_3
  38. Translate(A'_1, u) → N
  39. Segment(A'_3, N) → q'
  40. OrthogonalLine(A, r) → g_1
  41. Point(g_1) → O
  42. Angle(D, A, O) → α
  43. Angle(I', B, A) → β
  44. Rotate(A'_3, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → P
  45. Rotate(N, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → C
  46. Segment(P, C) → q''
  47. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], B) → A'_4
  48. Vector(A, A'_4) → v
  49. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
  50. Vector(D, I'_2) → w
  51. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], I') → A'_5
  52. Segment(A, A'_5) → i_1
  53. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], D) → A'_6
  54. Vector(A, A'_6) → u_1
  55. Translate(A, u_1) → A'_7
  56. Translate(A'_5, u_1) → Q
  57. Segment(A'_7, Q) → j_1
  58. Segment(D, B) → l_1
  59. Angle(L, A, I') → γ
  60. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → R
  61. Rotate(Q, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → Q'
  62. Segment(R, Q') → m_1
  63. Polygon(A, B, I', D) → poly1, a_2, c_2, i', i_2
  64. Intersect(i_1, m_1) → E
  65. Distance(A, E) → distanceAS
  66. Distance(E, C) → distanceSN'
  67. Distance(E, B) → distanceSC
  68. Distance(E, D) → distanceSI
  69. Angle(B, A, E) → δ
  70. Angle(E, B, A) → ε
  71. Angle(C, B, E) → ζ
  72. Angle(E, A, D) → η
  73. Angle(A, D, E) → θ
  74. Angle(E, D, C) → ι
  75. Angle(D, C, E) → κ
  76. Angle(B, E, C) → λ
  77. Angle(E, C, B) → μ
  78. Angle(A, E, B) → ν
  79. Polygon(A, B, C) → poly2, c_3, a_3, b_2
  80. Segment(A, C) → h_1
  81. Mirror(A, h_1) → A'_8
  82. Mirror(B, h_1) → B'
  83. Mirror(C, h_1) → C'
  84. Polygon(A'_8, B', C') → poly2', c', a'_8, b'
  85. Polygon(D, A, B) → poly3, b_3, d_2, a_4
  86. Segment(D, B) → p_1
  87. Mirror(D, p_1) → D'
  88. Mirror(A, p_1) → A'_9
  89. Mirror(B, p_1) → B'_1
  90. Polygon(D', A'_9, B'_1) → poly3', b'_1, d', a'_9