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Congruence and Transformations

Congruence and Transformations
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2018-12-03 10:48
Coordinate GeometryTransformationGeometric Construction
This example demonstrates congruent figures and their transformations. Key mathematical concepts include congruence and transformations (mirroring, rotating, dilating). Using GeoGebra commands such as Polygon, Line, Mirror, Rotate, and Dilate, the construction of congruent figures and their transformation processes is illustrated. Suitable for students at the junior high school level and above learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c_1, a_1, b_1
  2. Line(D, E) → f
  3. Mirror(A, f) → G
  4. Mirror(B, f) → H
  5. Mirror(C, f) → F
  6. Polygon(G, H, F) → t1', c', a', b'
  7. Polygon(B', C', A') → t2, k, i, j
  8. Textfield(A') → InputBox1
  9. Textfield(B') → InputBox2
  10. Textfield(C') → InputBox3
  11. Mirror(A, xAxis) → A'_1
  12. Mirror(B, xAxis) → B'_1
  13. Mirror(C, xAxis) → C'_1
  14. Polygon(A'_1, B'_1, C'_1) → t1'_1, c'_1, a'_1, b'_1
  15. Polygon(C'', A'', B'') → t3, k_1, i_1, j_1
  16. Textfield(A'') → InputBox4
  17. Textfield(B'') → InputBox5
  18. Textfield(C'') → InputBox6
  19. Polygon(I, J, K) → t4, k_2, i_2, j_2
  20. Polygon(I', K', J') → t5, n, l, m
  21. Intersect(xAxis, yAxis) → L
  22. Rotate(I, (-(90°)), L) → I'_1
  23. Rotate(J, (-(90°)), L) → J'_1
  24. Rotate(K, (-(90°)), L) → K'_1
  25. Polygon(I'_1, J'_1, K'_1) → t4', k'_1, i'_1, j'_1
  26. Rotate(I, 90°, L) → I'_2
  27. Rotate(J, 90°, L) → J'_2
  28. Rotate(K, 90°, L) → K'_2
  29. Polygon(I'_2, J'_2, K'_2) → t4'_1, k'_2, i'_2, j'_2
  30. Textfield(J') → InputBox7
  31. Textfield(K') → InputBox8
  32. Textfield(I') → InputBox9
  33. Polygon(M, N, O) → t6, o, m_1, n_1
  34. Textfield(M) → InputBox10
  35. Textfield(N) → InputBox11
  36. Textfield(O) → InputBox12
  37. Polygon(P, Q, R) → t7, r, p, q
  38. Polygon(P', R', Q') → t8, a_2, w, z_1
  39. Polygon(Z, A_1, B_1) → t9, b_2, z_2, a_3
  40. Dilate(Z, 2, W) → Z'
  41. Dilate(A_1, 2, W) → C_1
  42. Dilate(B_1, 2, W) → D_1
  43. Polygon(Z', C_1, D_1) → t9', d_1, z', c_2
  44. Polygon(E_1, F_1, G_1) → t10, g_1, e_1, f_1
  45. Textfield(E_1) → InputBox13
  46. Textfield(F_1) → InputBox14
  47. Textfield(G_1) → InputBox15