MathPlotAI Logo MathPlotAI

Equilateral Triangle Animation

Equilateral Triangle Animation
Loading the math board and drawing, please wait…
2016-06-29 09:10
TriangleTrigonometryGeometric 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
This example demonstrates the dynamic changes of an equilateral triangle. Key mathematical concepts include the properties of equilateral triangles, angles, and trigonometric functions. Using GeoGebra commands such as Line, Ray, Point, Rotate, Angle, Circle, etc., the dynamic changes of the equilateral triangle can be constructed. Suitable for students at the junior high school level and above to learn about geometric transformations and dynamic graphics.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Ray(A, B) → g
  3. Point(g) → C
  4. Rotate(C, π / 3, A) → C'
  5. Angle(C, A, C') → α
  6. Rotate(A, (-(π / 3)), C) → A'
  7. Angle(A', C, A) → β
  8. Circle(A, C) → c
  9. Circle(C, A) → d
  10. Intersect(c, d, 1) → D
  11. Segment(A, D) → h
  12. Segment(A, C) → i
  13. Segment(C, D) → j
  14. Circle(A, (0.15 * i)) → e
  15. Intersect(e, h, 1) → E
  16. Intersect(e, i, 1) → F
  17. CircleSector(A, F, E) → k
  18. Polygon(A, C, D) → poly1, d_1, a_1, c_1
  19. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C) → A'_1
  20. Segment(A, A'_1) → l
  21. Dilate(A, If[1 < a ≤ 2, 2 - a, 0], C) → A'_2
  22. Vector(A, A'_2) → u
  23. Translate(k, u) → k'
  24. Rotate(k', If[2 < a ≤ 3, (((a - 2) * 2) * π / 3), (2 * π / 3)], C) → k''
  25. Dilate(C, If[3 < a ≤ 4, 4 - a, 0], D) → C'_1
  26. Vector(C, C'_1) → v
  27. Translate(k'', v) → k'''
  28. Rotate(k''', If[4 < a ≤ 5, (((a - 4) * 2) * π / 3), (2 * π / 3)], D) → p
  29. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], A) → D'
  30. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], C) → D'_1
  31. Segment(D, D') → m
  32. Segment(D, D'_1) → n
  33. Rotate(A, If[6.5 < a ≤ 7.5, ((a - 6.5) * π / 3), π / 3], A) → A'_3
  34. Rotate(A'_1, If[6.5 < a ≤ 7.5, ((a - 6.5) * π / 3), π / 3], A) → G
  35. Segment(A'_3, G) → l'
  36. Rotate(A, If[7.5 < a ≤ 8.5, ((-(a - 7.5)) * π / 3), ((-π)) / 3], C) → A'_4
  37. Rotate(A'_1, If[7.5 < a ≤ 8.5, ((-(a - 7.5)) * π / 3), ((-π)) / 3], C) → H
  38. Segment(A'_4, H) → l'_1