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Comparing Size by Cut and Paste Q1

Comparing Size by Cut and Paste Q1
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2014-05-04 16:16
TrianglePolygonTransformationGeometric Construction
In collections P4 Area (I) P.4b_Area and Perimeter P.4b_Area and Perimeter
① This example demonstrates how to compare the sizes of two polygons (e.g., triangles or quadrilaterals) through a cut-and-paste visual approach, showing that area is preserved under rigid transformations. ② Core mathematical concepts include area comparison, dissection and reassembly, area conservation, and properties of polygon areas. ③ Construction details: Based on the construction summary, the GeoGebra commands used include Polygon, If, Point, Rotate, and Translate, creating multiple polygon objects (poly1 to poly7) and their copies, with rotations and translations to simulate cutting and pasting, and conditional objects (AonB, ConD) to control the comparison steps. ④ Suitable for upper elementary to middle school students, this interactive model aids in teaching geometric area concepts and can serve as a template for teachers to build dynamic lessons.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (10, 0), (10, 7), (0, 7)) → poly3, poly3_1, poly3_2, poly3_3, poly3_4
  2. Polygon((14, 0), (26, 0), (26, 6), (14, 6)) → poly1, a, b, c, d
  3. Polygon(A, A + (12, 0), A + (12, 6), A + (0, 6)) → poly2, poly2_1, poly2_2, poly2_3, poly2_4
  4. If(A ≟ B, true, false) → AonB
  5. Polygon((0, 0), (10, 0), (10, 6), (0, 6)) → poly4, poly4_1, poly4_2, poly4_3, poly4_4
  6. Point(CircleArc[(5, 1), (10, 6), (0, 6)]) → C
  7. Rotate(Polygon[(10, 0), (12, 0), (12, 6), (10, 6)], Angle[(10, 6), (5, 1), C], (5, 1)) → poly5
  8. Rotate(Segment[(10, 0), (12, 0)], Angle[(10, 6), (5, 1), C], (5, 1)) → poly5_1
  9. Rotate(Segment[(12, 0), (12, 6)], Angle[(10, 6), (5, 1), C], (5, 1)) → poly5_2
  10. Rotate(Segment[(12, 6), (10, 6)], Angle[(10, 6), (5, 1), C], (5, 1)) → poly5_3
  11. Rotate(Segment[(10, 0), (10, 6)], Angle[(10, 6), (5, 1), C], (5, 1)) → poly5_4
  12. If(C ≟ D, true, false) → ConD
  13. Polygon((0, 6), (6, 6), (6, 7), (0, 7)) → poly6, poly6_1, poly6_2, poly6_3, poly6_4
  14. Polygon(E, E + (6, 0), E + (6, 1), E + (0, 1)) → poly7, poly7_1, poly7_2, poly7_3, poly7_4
  15. If(E ≟ F, true, false) → EonF
  16. Translate(Polygon[(0, 0), (10, 0), (10, 6), (0, 6)], Vector[(0, 0), (14 * t, 0)]) → poly8
  17. Translate((0, 6), Vector[(0, 0), (24 * t, 0)]) → G
  18. Rotate(G + (6, 0), (-90)° * t, G) → H
  19. Polygon(G, H, I, J) → poly9, poly9_1, poly9_2, poly9_3, poly9_4
  20. Translate((6, 6), Vector[(0, 0), (19 * t, 0)]) → K
  21. Rotate(K + (4, 0), (-90)° * t, K) → L
  22. Polygon(K, L, M, N) → poly10, poly10_1, poly10_2, poly10_3, poly10_4
  23. Translate(Polygon[(0, 0), (10, 0), (10, 6), (0, 6)], Vector[(0, 0), (14 * t, 0)]) → poly11
  24. Polygon(O, O + (2, 0), O + (2, 1), O + (0, 1)) → poly12, poly12_4, poly12_1, poly12_2, poly12_3
  25. Translate(O, Vector[t * Vector[O, (25, 2)]]) → O'
  26. Rotate(O' + (2, 0), (-90)° * t, O') → P
  27. Polygon(O', P, Q, R) → poly13, poly13_3, poly13_4, poly13_1, poly13_2

AI Drawing Prompt Reference

Create an interactive geometry diagram showing area comparison of two polygons through cut-and-paste. Place a rectangle on the left and another on the right with different heights. On the left rectangle, use a movable point to control rotation of a vertical strip around a pivot, simulating cutting. Meanwhile, use sliders to translate parts of the rectangle horizontally and rotate them to form new shapes, which can be pasted onto another figure, visually demonstrating that area is preserved. Include multiple polygons whose positions and rotations are controlled by sliders, and add conditional checks for point coincidences to show comparison steps. The layout should be clear for educational purposes.
The prompt above was compiled from the original drawing commands and is for reference only.