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Congruence via Rigid Motions by Hannah

Congruence via Rigid Motions by Hannah
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2016-09-22 08:35
VectorTransformationGeometric Construction
This example demonstrates how geometric figures can be made congruent through rigid motions such as translation, rotation, and reflection. Key math concepts include congruence, geometric transformations, vectors, line segments, and complex numbers. Construction highlights the use of GeoGebra commands like Point, Polygon, Intersect, Line, Mirror, Rotate, Vector, and Translate. Suitable for high school students studying geometric transformations and congruence.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 3.605551275463989]) → B
  2. Polygon(A, B, C_1) → poly1, c, a, b
  3. Point(Circle[X, 3.605551275463989]) → Y
  4. Polygon(X, Y, F_1) → poly2, f, d, e
  5. Intersect(a, b) → C
  6. Intersect(d, e) → Z
  7. Line(G_1, I_1) → g
  8. Mirror(A, g) → F
  9. Mirror(B, g) → D
  10. Mirror(C_1, g) → J_1
  11. Polygon(F, D, J_1) → poly1', j, a', b'
  12. Intersect(a', b') → E
  13. Rotate(A, 140°, K_1) → H
  14. Rotate(B, 140°, K_1) → I
  15. Rotate(C_1, 140°, K_1) → L_1
  16. Polygon(H, I, L_1) → poly1'_1, l, a'_1, b'_1
  17. Intersect(a'_1, b'_1) → G
  18. Vector(J_2, M_1) → u
  19. Translate(A, u) → J
  20. Translate(B, u) → K
  21. Translate(C_1, u) → N_1
  22. Polygon(J, K, N_1) → poly1'_2, n, a'_2, b'_2
  23. Intersect(a'_2, b'_2) → L
  24. Point(Circle[P, 4.40953512288994]) → Q
  25. Polygon(P, Q, Q_1) → poly3, q, o, p
  26. Point(Circle[M, 4.88069667158286]) → O
  27. Polygon(M, O, T_1) → poly4, t, r, s
  28. Point(Circle[S, 4.204045670541651]) → T
  29. Polygon(S, T, W) → poly5, w, u_1, v
  30. Intersect(u_1, v) → U
  31. Intersect(o, p) → R
  32. Intersect(r, s) → N