MathPlotAI Logo MathPlotAI

Isosceles Trapezoid Template by Tim Brzezinski

Isosceles Trapezoid Template by Tim Brzezinski
Loading the math board and drawing, please wait…
2016-10-12 03:20
PolygonAngleVector
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 geometric construction and properties of an isosceles trapezoid. It involves core mathematical concepts such as polygons, angles, vectors, and geometric transformations. The construction utilizes GeoGebra commands and objects like Line, Point, Midpoint, Slope, OrthogonalLine, Mirror, Dilate, Segment, Circle, Intersect, Vector, Translate, Angle, Rotate, Polygon, and Distance. It is suitable for high school mathematics teaching or geometric construction practice, helping to understand the symmetry and transformation properties of isosceles trapezoids.

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') → C
  34. Segment(D, C) → 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_1
  46. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], B) → A'_4
  47. Vector(A, A'_4) → v
  48. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
  49. Vector(D, I'_2) → w
  50. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], I') → A'_5
  51. Segment(A, A'_5) → i_1
  52. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], D) → A'_6
  53. Vector(A, A'_6) → u_1
  54. Translate(A, u_1) → A'_7
  55. Translate(A'_5, u_1) → Q
  56. Segment(A'_7, Q) → j_1
  57. Segment(D, B) → l_1
  58. Angle(L, A, I') → γ
  59. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → R
  60. Rotate(Q, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → Q'
  61. Segment(R, Q') → m_1
  62. Polygon(A, B, I', D) → poly1, a_2, c_2, i', i_2
  63. Intersect(i_1, m_1) → E
  64. Distance(A, E) → distanceAS
  65. Distance(E, C_1) → distanceSN'
  66. Distance(E, B) → distanceSC
  67. Distance(E, D) → distanceSI
  68. Segment(B, I') → q''