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Area of a Parallelogram by Ms. Muusse

Area of a Parallelogram by Ms. Muusse
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2018-07-01 09:42
PolygonCoordinate GeometryGeometric Construction
This example dynamically illustrates that the area of a parallelogram is equal to the area of a rectangle with the same base and height. Key concepts include the properties of parallelograms and area calculation methods. Using GeoGebra commands such as Line, Segment, Polygon, etc., the principle of equal area can be intuitively understood. Suitable for students at the junior high school level and above.

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

AI Drawing Prompt Reference

Draw a parallelogram and demonstrate that its area is equal to the area of a rectangle with the same base and height. Start by drawing the base AB of the parallelogram, then draw a line f1 through points A and B. Next, take a point C on line f1 and draw a line f parallel to AB through C, intersecting at point H. Connect CH and draw a line q perpendicular to CH, intersecting AB at point I. Then, draw a circle g1 centered at B with radius BI, intersecting line f1 at point M. Connect AC and draw a line p parallel to AB through C, intersecting f at point G. Connect GE and draw a circle s centered at G with radius GE, intersecting AB at point L. Finally, draw parallelograms ACIJ, JBEI, CLIK, and LEJK, and adjust the position of point I to show equal areas.
The prompt above was compiled from the original drawing commands and is for reference only.