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Congruent Segments Demo

Congruent Segments Demo
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2016-10-31 13:18
VectorTransformationGeometric Construction
In collections Congruence Review 1
This example dynamically illustrates the transformational geometry definition of segment congruence using vectors and transformations. Key math concepts include segment congruence, geometric transformations (translation, rotation), and vector operations. Constructed with GeoGebra commands like Segment, Point, Vector, Translate, Rotate. Suitable for middle school and above students to learn geometric transformations and congruence criteria.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Point(Circle[C, a]) → D
  3. Segment(C, D) → b
  4. Dilate(A, If[0 < c ≤ 1, 1 - c, 0], D) → A'
  5. Vector(A, A') → u
  6. Line(A, D) → d
  7. Vector(A, D) → v
  8. Translate(A, v) → A'_2
  9. Translate(B, v) → B'_1
  10. Segment(A'_2, B'_1) → a'_1
  11. Angle(C, D, B'_1) → α
  12. Translate(A, u) → A'_1
  13. Translate(B, u) → B'
  14. Segment(A'_1, B') → a'
  15. Rotate(A'_1, If[1 < c ≤ 2, ((-(c - 1)) * α), (-α)], A'_1) → E
  16. Rotate(B', If[1 < c ≤ 2, ((-(c - 1)) * α), (-α)], A'_1) → B''
  17. Segment(E, B'') → a''
  18. Circle(D, 1) → e
  19. Intersect(e, a'_1, 1) → F
  20. Intersect(e, b, 1) → G
  21. Intersect(e, a'_1, 1) → H
  22. Intersect(e, a'', 1) → I
  23. CircleSector(D, I, H) → f

AI Drawing Prompt Reference

Draw a triangle ABC with line segments AB and CD being congruent. Draw a circle with AB as the diameter and find point D on the circle such that CD is congruent to AB. Then, rotate line segment AB around point D to get line segment A'B'. Translate line segment A'B' to be parallel to AB to get line segment a'. Finally, draw line segment A'B' through points A' and B', and rotate it around point A' to get line segment A''B''.
The prompt above was compiled from the original drawing commands and is for reference only.