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Dynamic Demonstration of Isosceles Triangles and Parallelograms

Dynamic Demonstration of Isosceles Triangles and Parallelograms
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2016-06-14 22:27
TriangleTransformationGeometric ConstructionSlider Animation
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 isosceles triangles and parallelograms. Key mathematical concepts include the properties of isosceles triangles and parallelograms. Using GeoGebra commands such as Circle, Intersect, CircleArc, Point, Dilate, Segment, Angle, Rotate, Midpoint, CircleSector, Polygon, Vector, Translate, the dynamic geometric figures can be constructed. Suitable for middle and high school students to learn geometric transformations and dynamic geometry.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Intersect(c, q) → O, P
  3. CircleArc(A, O, P) → d
  4. Point(d) → C
  5. CircleArc(A, C, P) → e
  6. Point(e) → D
  7. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
  8. Segment(A, A') → a
  9. Angle(C, A, D) → α
  10. Rotate(A, If[1 < j ≤ 2, ((j - 1) * α), α], A) → A'_1
  11. Rotate(A', If[1 < j ≤ 2, ((j - 1) * α), α], A) → A''
  12. Segment(A'_1, A'') → a'
  13. Segment(A, C) → b
  14. Segment(C, D) → f
  15. Segment(D, A) → g
  16. Midpoint(f) → E
  17. Segment(A, E) → h
  18. Midpoint(h) → F
  19. Segment(A, F) → i
  20. Segment(F, E) → k
  21. Circle(A, (0.35 * i)) → p
  22. Circle(E, (0.15 * Distance[D, E])) → r
  23. Intersect(r, f, 2) → G
  24. Intersect(r, h, 1) → H
  25. Intersect(r, f, 1) → I
  26. Intersect(p, b, 1) → J
  27. Intersect(p, h, 1) → K
  28. Intersect(p, g, 1) → L
  29. CircleSector(A, K, L) → s
  30. CircleSector(E, G, H) → t
  31. Circle(A, B) → c_1
  32. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], D) → C'
  33. Segment(C, C') → l
  34. Polygon(C, D, A) → poly1, a_1, c_2, d_1
  35. Circle(C, (0.2 * Distance[D, E])) → e_1
  36. Intersect(e_1, b) → M,
  37. Intersect(e_1, f) → N,
  38. CircleSector(C, N, M) → f_1
  39. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], F) → A'_2
  40. Segment(A, A'_2) → m
  41. Rotate(s, If[4 < j ≤ 5, ((-(j - 4)) * α / 2), ((-α)) / 2], A) → s'
  42. Dilate(F, If[5 < j ≤ 6, 6 - j, 0], E) → F'
  43. Segment(F, F') → n
  44. CircleArc(A, K, L) → g_1
  45. Dilate(E, If[6 < j ≤ 7, 7 - j, 0], D) → E'
  46. Segment(E, E') → b_1
  47. Rotate(E, If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E'_1
  48. Rotate(E', If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E''
  49. Segment(E'_1, E'') → h_1
  50. Rotate(t, If[8 < j ≤ 9, ((j - 8) * π / 2), 1.5707963267948966], E) → t'
  51. CircleArc(E, G, H) → k_1
  52. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], D) → C'_1
  53. Vector(C, C'_1) → u
  54. Translate(f_1, u) → p_1
  55. CircleArc(C, N, M) → q_1
  56. Angle(E, C, A) → β
  57. Rotate(p_1, If[10 < j ≤ 11, ((j - 10) * (π - β)), π - β], D) → r_1

AI Drawing Prompt Reference

Draw an isosceles triangle and a parallelogram, and use a slider to dynamically change their shapes. Start by drawing an isosceles triangle ABC, then construct parallelogram ACDE using points A, C, and D. Apply rotation and translation commands to change the size and position of the triangle and parallelogram, observing their properties as they change.
The prompt above was compiled from the original drawing commands and is for reference only.