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Illustration of Congruent Line Segments

Illustration of Congruent Line Segments
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2018-08-26 13:17
VectorTransformationGeometric Construction
This applet illustrates the transformational geometry definition of segment congruence. Key mathematical concepts include segment congruence, rotation, and translation. Using GeoGebra commands such as Segment, Dilate, Translate, and Rotate, students can visually understand these transformations. Suitable for middle school and above students learning geometric transformations.

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