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Proportional Relationship Between Squares and Rectangles

Proportional Relationship Between Squares and Rectangles
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2014-04-26 12:15
Geometric ConstructionSlider Animation
This example demonstrates the proportional relationship between squares and rectangles. Key mathematical concepts include proportion and geometric construction. Using GeoGebra commands such as Integral, Polygon, Intersect, etc., the proportional squares and rectangles can be constructed. Suitable for middle school and above students to learn about geometric proportions and transformations.

GeoGebra Commands & Parameters

  1. Integral(acceleration) → velocity
  2. Polygon(A, B, 4) → poly1, b_1, c, d, e, C, D
  3. Integral(velocity_m) → distance_m
  4. Polygon(A', B', C', D') → poly2, a', b', c', d'
  5. Intersect(distance_m, b', 1) → M
  6. Polygon(A', C'', B') → poly3, k, l, m
  7. Segment(B', M) → b
  8. Point(b) → E
  9. OrthogonalLine(E, xAxis) → g
  10. OrthogonalLine(E, g) → h
  11. Circle(E, b) → p
  12. Intersect(p, g) → F, G
  13. OrthogonalLine(G, g) → i
  14. Intersect(i, yAxis) → H
  15. Intersect(h, yAxis) → I
  16. Polygon(I, E, G, H) → poly4, i_1, e_1, g_1, h_1

AI Drawing Prompt Reference

Draw a square and a rectangle proportional to it. Start by creating a slider for the proportion factor. Then, construct a square using this slider. Next, construct a rectangle proportional to the square, with one side proportional to the square's side. Finally, use intersection points and perpendicular lines to complete the rectangle, ensuring the correct proportion.
The prompt above was compiled from the original drawing commands and is for reference only.