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Congruence Practice #2

Congruence Practice #2
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2017-09-22 10:32
TriangleTransformationGeometric Construction
This example demonstrates how to prove the congruence of geometric figures through transformations such as rotation, translation, and reflection. Key math concepts include congruence, geometric transformations, vectors, and polygon construction. GeoGebra commands and objects used are Point, Polygon, Rotate, Vector, Translate, Line, Intersect, Mirror. Suitable for high school students practicing geometric proofs and transformation applications.

GeoGebra Commands & Parameters

  1. Point(xAxis) → D
  2. Polygon(A, B, C, D, E, F) → poly1, a, b, c, d, e, f
  3. Rotate(A, 90°, B) → A'
  4. Rotate(B, 90°, B) → B'
  5. Rotate(C, 90°, B) → C'
  6. Rotate(D, 90°, B) → D'
  7. Rotate(E, 90°, B) → E'
  8. Rotate(F, 90°, B) → F'
  9. Polygon(A', B', C', D', E', F') → poly1', a', b', c', d', e', f'
  10. Vector(F', G) → u
  11. Translate(A', u) → A''
  12. Translate(B', u) → B''
  13. Translate(C', u) → C''
  14. Translate(D', u) → D''
  15. Translate(E', u) → E''
  16. Translate(F', u) → F''
  17. Polygon(A'', B'', C'', D'', E'', F'') → poly1'', a'', b'', c'', d'', e'', f''
  18. Line(H, I) → g
  19. Intersect(xAxis, yAxis) → J
  20. Line(J, K) → h
  21. Mirror(A, h) → A'_1
  22. Mirror(B, h) → B'_1
  23. Mirror(C, h) → C'_1
  24. Mirror(D, h) → D'_1
  25. Mirror(E, h) → E'_1
  26. Mirror(F, h) → F'_1
  27. Polygon(A'_1, B'_1, C'_1, D'_1, E'_1, F'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1, e'_1, f'_1
  28. Vector(F'_1, L) → v
  29. Translate(A'_1, v) → M
  30. Translate(B'_1, v) → N
  31. Translate(C'_1, v) → O
  32. Translate(D'_1, v) → P
  33. Translate(E'_1, v) → Q
  34. Translate(F'_1, v) → R
  35. Polygon(M, N, O, P, Q, R) → poly2, m, n, o, p, q, r