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Visual Proof of Parallelogram

Visual Proof of Parallelogram
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2023-03-19 01:21
PolygonTransformationGeometric Construction
In collections geometriadinamica.es
This example demonstrates a visual proof of a parallelogram. Key mathematical concepts include geometric construction and transformation. Using GeoGebra commands such as Rotate, Ray, Point, Polygon, and Sequence, the construction of a parallelogram and its related elements is illustrated. Suitable for middle school and above students to learn about geometric transformations and proof methods.

GeoGebra Commands & Parameters

  1. Rotate(B, α, A) → B'
  2. Ray(A, B') → a
  3. Point(a) → C
  4. Rotate(A, (2 * 3.141592653589793 / (n - 1)), C) → A'
  5. Polygon(A, A', n - 1) → poly1, b, G, c, d, g, g_1, h_1, D, E, F
  6. Sequence(Dilate[A, 1 / (sqrt(n))^(k), C], k, 1, o) → list2
  7. Sequence(Dilate[A', 1 / (sqrt(n))^(k), C], k, 1, o) → list1
  8. Polygon(A, A', Element[list1, 1], Element[list2, 1]) → poly2, a_1, a', e, f
  9. Polygon(Element[list1, 1], Element[list2, 1], Element[list2, 2], Element[list1, 2]) → poly3, h, j, k, l
  10. Polygon(Element[list1, 3], Element[list2, 3], Element[list2, 2], Element[list1, 2]) → poly4, r, s, t, b_1
  11. Polygon(Element[list1, 3], Element[list2, 3], Element[list2, 4], Element[list1, 4]) → poly5, c_1, d_1, e_1, f_1
  12. Sequence(Segment[Rotate[A', ((2 * k) * 3.141592653589793 / (n - 1)), C], Rotate[Element[list1, 1], ((2 * k) * 3.141592653589793 / (n - 1)), C]], k, 1, n - 3) → list3
  13. Sequence(Segment[Rotate[Element[list1, 1], ((2 * k) * 3.141592653589793 / (n - 1)), C], Rotate[Element[list2, 1], ((2 * k) * 3.141592653589793 / (n - 1)), C]], k, 1, n - 2) → list4
  14. Sequence(Segment[Rotate[Element[list1, 2], ((2 * k) * 3.141592653589793 / (n - 1)), C], Rotate[Element[list1, 1], ((2 * k) * 3.141592653589793 / (n - 1)), C]], k, 1, n - 3) → list5
  15. Sequence(Segment[Rotate[Element[list2, 2], ((2 * k) * 3.141592653589793 / (n - 1)), C], Rotate[Element[list1, 2], ((2 * k) * 3.141592653589793 / (n - 1)), C]], k, 1, n - 2) → list6
  16. Sequence(Segment[Rotate[Element[list1, 2], ((2 * k) * 3.141592653589793 / (n - 1)), C], Rotate[Element[list1, 3], ((2 * k) * 3.141592653589793 / (n - 1)), C]], k, 1, n - 3) → list7
  17. Sequence(Segment[Rotate[Element[list1, 3], ((2 * k) * 3.141592653589793 / (n - 1)), C], Rotate[Element[list2, 3], ((2 * k) * 3.141592653589793 / (n - 1)), C]], k, 1, n - 2) → list8
  18. Polygon(Element[list1, 5], Element[list2, 5], Element[list2, 4], Element[list1, 4]) → poly6, i, m, p, q

AI Drawing Prompt Reference

Draw a visual proof of a parallelogram, including a parallelogram and its related elements. First, draw a line segment, then rotate a point to get a new point. Next, draw a ray to get a point. Again, rotate a point to get another new point. Then, draw a polygon to get a parallelogram and some other points. Next, perform several dilations and rotations to get some line segments and polygons. Finally, draw the related elements of the parallelogram, including some line segments and polygons.
The prompt above was compiled from the original drawing commands and is for reference only.