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Dynamic Construction of Equilateral Triangles and Parallelograms via Vector Tran

Dynamic Construction of Equilateral Triangles and Parallelograms via Vector Tran
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2016-06-14 21:30
TriangleCirclePolygonVectorTransformation
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
This example demonstrates the dynamic geometric relationship between equilateral triangles and parallelograms using vector translation and rotation transformations. Core concepts involve vector operations, geometric transformations, polygon properties, and circumcircles. Construction utilizes GeoGebra commands such as Vector, Translate, Rotate, Dilate, and Polygon, combining points A, B, C with their transformed counterparts A', B', C'. It is suitable for middle school geometry teaching or mathematical competition exploration of figure transformations, helping students intuitively understand spatial structures.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Slope(a) → m
  3. PointIn(c) → C
  4. Line(C, a) → e
  5. Vector(A, B) → u
  6. Translate(C, u) → C'
  7. Segment(B, C') → f
  8. Segment(C, C') → g
  9. Segment(A, B) → h
  10. Segment(A, C) → d
  11. Midpoint(A, C') → D
  12. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], D) → A'
  13. Segment(A, A') → i
  14. Dilate(D, If[1 < k ≤ 2, 2 - k, 0], C') → D'
  15. Segment(D, D') → l
  16. Dilate(C, If[2 < k ≤ 3, 3 - k, 0], D) → C'_1
  17. Segment(C, C'_1) → j
  18. Dilate(D, If[3 < k ≤ 4, 4 - k, 0], B) → D'_1
  19. Segment(D, D'_1) → n
  20. Rotate(D, If[5 < k ≤ 6, ((k - 5) * π), 3.141592653589793], D) → D'_2
  21. Rotate(D', If[4 < k ≤ 5, ((k - 4) * π), 3.141592653589793], D) → D''
  22. Segment(D'_2, D'') → l'
  23. Rotate(D, If[6 < k ≤ 7, ((k - 6) * π), 3.141592653589793], D) → D'_3
  24. Rotate(D'_1, If[5 < k ≤ 6, ((k - 5) * π), 3.141592653589793], D) → E
  25. Segment(D'_3, E) → n'
  26. Rotate(A, If[6 < k ≤ 7, ((-(k - 6)) * π), -3.141592653589793], D) → A'_1
  27. Rotate(B, If[6 < k ≤ 7, ((-(k - 6)) * π), -3.141592653589793], D) → B'
  28. Polygon(A, B, C', C) → poly1, a_1, b_1, c', c_1