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Divide a Rectangle into Two Equal Parts

Divide a Rectangle into Two Equal Parts
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2016-03-10 03:53
PolygonGeometric Construction
This example demonstrates how to divide a rectangle into two equal parts. Key mathematical concepts include ratios and line segments. Using GeoGebra commands such as Point, Line, Intersect, Segment, and Polygon, the construction process is visually illustrated. Suitable for middle school and above students to learn geometric construction and ratio concepts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Line(A, B) → a
  3. OrthogonalLine(A, a) → b
  4. OrthogonalLine(B, a) → c
  5. Point(c) → C
  6. OrthogonalLine(C, c) → d
  7. Intersect(b, d) → D
  8. Line(A, C) → e
  9. Line(B, D) → f
  10. Intersect(e, f) → E
  11. Circle(E, A) → g
  12. Point(g) → GrabandDrag
  13. Line(GrabandDrag, E) → h
  14. Intersect(g, h) → G, H
  15. Segment(GrabandDrag, H) → i
  16. Intersect(c, i) → I
  17. Intersect(b, i) → J
  18. Polygon(D, C, I, J) → poly1, d_1, c_1, i_1, j
  19. PointIn(poly1) → Pointpoly1
  20. Polygon(B, I, J, A) → poly2, b_1, i_2, j_1, a_1
  21. PointIn(poly2) → Pointpoly2
  22. Intersect(a, i) → K
  23. Intersect(d, i) → L
  24. Polygon(K, B, C, L) → poly3, k, b_2, c_2, l
  25. PointIn(poly3) → Pointpoly3
  26. Polygon(D, L, K, A) → poly4, d_2, l_1, k_1, a_2
  27. PointIn(poly4) → Pointpoly4
  28. Perimeter(Polygon[(1, 10), (1, 0), (6.17, 0), (10.83, 10)]) → m
  29. Distance(A, K) → distanceAK
  30. Midpoint(A, K) →
  31. Distance(K, L) → distanceKL
  32. Midpoint(K, L) →
  33. Distance(L, D) → distanceLD
  34. Midpoint(L, D) →
  35. Distance(D, A) → distanceDA
  36. Midpoint(D, A) →
  37. Distance(B, I) → distanceBI
  38. Midpoint(B, I) →
  39. Distance(I, J) → distanceIJ
  40. Midpoint(I, J) →
  41. Distance(J, A) → distanceJA
  42. Midpoint(J, A) →
  43. Distance(A, B) → distanceAB
  44. Midpoint(A, B) →

AI Drawing Prompt Reference

Draw a rectangle and divide it into two equal parts. First, draw a horizontal line through the center of the rectangle, then draw a vertical line through the center. The intersection of these two lines will divide the rectangle into four equal sections. Next, connect the midpoints of the diagonals, forming two lines that will divide the rectangle into two equal parts.
The prompt above was compiled from the original drawing commands and is for reference only.