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Area of a Parallelogram by Mrs. Cole

Area of a Parallelogram by Mrs. Cole
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2019-03-26 10:33
PolygonGeometric Construction
This dynamic illustration demonstrates that the area of a parallelogram is equal to the area of a rectangle with the same base and height. Key mathematical concepts include parallelograms, rectangles, and area calculation. Using GeoGebra commands such as Line, Segment, and Polygon, the equivalence of areas can be visually understood. Suitable for middle school and above students learning geometry.

GeoGebra Commands & Parameters

  1. Line(A, B) → f_1
  2. Line(A, B) → b
  3. Slope(b) → m
  4. PointIn(d) → C
  5. Segment(A, B) → a
  6. Line(C, a) → f
  7. OrthogonalLine(B, f) → n
  8. Intersect(f, n) → H
  9. Segment(C, H) → l
  10. Point(l) → I
  11. OrthogonalLine(I, l) → q
  12. Intersect(q, a) → J
  13. Circle(B, Distance[A, J]) → g_1
  14. Intersect(g_1, f_1, 2) → M
  15. Segment(A, C) → e
  16. Point(f) → D
  17. Ray(C, D) → g
  18. Line(B, e) → h
  19. Intersect(h, g) → E
  20. Segment(C, E) → i
  21. Segment(B, E) → j
  22. Point(i) → F
  23. OrthogonalLine(A, i) → k
  24. Angle(B, A, C) → α
  25. Ray(C, E) → p
  26. Intersect(f, k) → G
  27. Segment(G, E) → r
  28. Point(r) → K
  29. OrthogonalLine(K, r) → s
  30. Intersect(s, a) → L
  31. Polygon(A, J, I, C) → poly1, a_1, j_1, i_1, c_1
  32. Polygon(J, B, E, I) → poly2, j_2, b_1, e_1, i_2
  33. Polygon(A, L, K, C) → poly3, a_2, l_1, k_1, c_2
  34. Polygon(L, B, E, K) → poly4, l_2, b_2, e_2, k_2
  35. Dilate(I, If[0 < o ≤ 1, 1 - o, 0], J) → I'
  36. Segment(I, I') → t
  37. Angle(J, I, E) → β
  38. Dilate(J, If[2 < o ≤ 3, 3 - o, 0], M) → J'
  39. Vector(J, J') → u
  40. Angle(B, J, I) → γ
  41. OrthogonalLine(E, b) → d_1
  42. Translate(A, u) → A'
  43. Translate(J, u) → J'_1
  44. Translate(I, u) → I'_1
  45. Translate(C, u) → C'
  46. Polygon(A', J'_1, I'_1, C') → poly1', a', j'_1, i'_1, c'
  47. Angle(I'_1, J', J) → δ
  48. Polygon(A, B, E, C) → poly5, a_3, b_3, e_3, c_3
  49. Circle(E, Distance[C, K]) → h_1
  50. Intersect(h_1, f, 2) → N
  51. Polygon(A, B, E, C) → poly6, a_4, b_4, e_4, c_4
  52. Dilate(K, If[0 < o ≤ 1, 1 - o, 0], L) → K'
  53. Segment(K, K') → m_1
  54. Angle(L, K, E) → ε
  55. Angle(B, L, K) → ζ
  56. Dilate(K, If[2 < o ≤ 3, 3 - o, 0], N) → K'_1
  57. Vector(K, K'_1) → v
  58. Translate(A, v) → A'_1
  59. Translate(L, v) → L'
  60. Translate(K, v) → K'_2
  61. Translate(C, v) → C'_1
  62. Polygon(A'_1, L', K'_2, C'_1) → poly3', a'_1, l', k'_2, c'_1
  63. Angle(K'_1, L', A) → η
  64. Segment(J'_1, I'_1) → n_1
  65. Segment(L', K'_2) → p_1