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Which Square is Bigger?

Which Square is Bigger?
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2020-07-11 01:43
PolygonTransformationGeometric Construction
This example demonstrates the comparison of two squares within pentagons. Through geometric construction, students can understand the concept of similarity transformation. Commands used include point, polygon, midpoint, orthogonal line, intersection, segment, circle, angular bisector, vector, translation, and rotation. Suitable for middle school and above students to learn about geometric transformations and similarity.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Polygon(A, B, 5) → polígono1, f, g, h, i, j, C, D, E
  3. Midpoint(A, B) → F
  4. Midpoint(D, F) → G
  5. OrthogonalLine(G, yAxis) → k
  6. Intersect(g, k) → H
  7. Intersect(j, k) → I
  8. Polygon(F, H, D, I) → c1, f_1, h_1, d, i_1
  9. Point(xAxis) → J
  10. Point(xAxis) → K
  11. Polygon(J, K, 5) → polígono2, l, m, n, p, q, L, M, N
  12. Midpoint(J, K) → O
  13. Midpoint(M, O) → P
  14. Midpoint(L, K) → Q
  15. Segment(N, Q) → r
  16. Segment(M, O) → s
  17. Intersect(r, s) → R
  18. Circle(R, Q) → c
  19. Point(n) → S
  20. OrthogonalLine(S, xAxis) → t
  21. OrthogonalLine(S, t) → a
  22. Intersect(p, a) → T
  23. OrthogonalLine(T, a) → b
  24. Intersect(t, m) → U
  25. Intersect(b, q) → V
  26. Polygon(V, U, S, T) → c2, v, u, s_1, t_1
  27. Midpoint(S, V) → W
  28. Segment(D, F) → e
  29. Segment(S, V) → g_1
  30. AngularBisector(C, B, A) → j_1
  31. AngularBisector(B, A, E) → k_1
  32. Intersect(k_1, j_1) → Z
  33. Segment(E, Z) → l_1
  34. Segment(Z, C) → m_1
  35. Segment(Z, B) → n_1
  36. Segment(Z, A) → p_1
  37. AngularBisector(K, J, N) → q_1
  38. AngularBisector(J, N, M) → r_1
  39. Intersect(r_1, q_1) → A_1
  40. Segment(N, A_1) → a_1
  41. Segment(A_1, M) → b_1
  42. Segment(A_1, L) → c_1
  43. Segment(A_1, K) → d_1
  44. Segment(A_1, J) → e_1
  45. Vector(V, V') → w
  46. Translate(V, w) → V'_3
  47. Translate(U, w) → U'_2
  48. Translate(S, w) → S'_2
  49. Translate(T, w) → T'_1
  50. Rotate(V, ((2 * π) * tras / 8), V) → V'_1
  51. Rotate(U, ((2 * π) * tras / 8), V) → U'
  52. Rotate(S, ((2 * π) * tras / 8), V) → S'
  53. Rotate(T, ((2 * π) * tras / 8), V) → T'
  54. Polygon(V'_1, U', S', T') → c2', v'_1, u', s', t'
  55. Translate(V'_1, w) → B_1
  56. Translate(U', w) → U''
  57. Translate(S', w) → S''
  58. Translate(T', w) → T''
  59. Polygon(B_1, U'', S'', T'') → c2'', f_2, u'', s'', t''