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Shearing a Triangle and a Parallelogram

Shearing a Triangle and a Parallelogram
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2016-02-03 23:35
TrianglePolygonTransformationGeometric Construction
This example demonstrates the shearing transformation applied to a triangle and a parallelogram, showing how the shapes change while preserving their areas. Students can explore the effects of shear using dynamic geometry, observing how vertices, sides, and angles move under the transformation. Key concepts include linear transformations, vector representation, area invariance, and shape congruence. The GeoGebra construction uses commands such as Line, Segment, Intersect, Point, and Polygon to create an interactive model. It is suitable for high‑school geometry, transformation geometry, and dynamic mathematics courses.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Segment(A, C) → b
  3. Line(C, a) → c
  4. Line(B, b) → d
  5. Intersect(c, d) → D
  6. Segment(D, B) → e
  7. Point(a) → E
  8. Point(a) → F
  9. Segment(E, F) → f
  10. Point(c) → G
  11. Segment(F, G) → g
  12. Segment(G, E) → h
  13. Point(h) → H
  14. Point(h) → I
  15. Point(h) → J
  16. Point(h) → K
  17. Point(h) → L
  18. Point(h) → M
  19. Line(H, f) → i
  20. Line(I, i) → j
  21. Line(J, j) → k
  22. Line(J, k) → l
  23. Line(K, h) → m
  24. Line(K, k) → n
  25. Line(L, n) → p
  26. Line(M, h) → q
  27. Line(M, p) → r
  28. Intersect(i, g) → N
  29. Segment(H, N) → s
  30. Intersect(j, g) → O
  31. Segment(I, O) → t
  32. Point(g) → P
  33. Segment(P, J) → a_1
  34. Intersect(n, g) → Q
  35. Segment(Q, K) → b_1
  36. Intersect(p, g) → R
  37. Segment(R, L) → c_1
  38. Intersect(r, g) → S
  39. Segment(S, M) → d_1
  40. Line(T, a) → e_1
  41. Line(U, a) → f_1
  42. Point(e_1) → V
  43. Point(f_1) → W
  44. Segment(V, W) → g_1
  45. Point(f_1) → Z
  46. Line(Z, g_1) → h_1
  47. Line(Z, g_1) → i_1
  48. Intersect(e_1, i_1) → A_1
  49. Segment(A_1, Z) → j_1
  50. Polygon(V, W, Z, A_1) → poly1, v, w, z_1, a_2
  51. Polygon(G, E, F) → poly2, f_2, g_2, e_2
  52. Polygon(I, H, N, O) → poly3, i_2, h_2, n_1, o