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Rectangle Ratios Demo

Rectangle Ratios Demo
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2020-07-27 20:50
TrianglePolygonProbability & StatisticsTransformationGeometric Construction
This example demonstrates the ratio relationships between rectangles, triangles, and equilateral triangles, involving geometric transformations like orthogonal lines and rotations. Core math concepts include plane figures, rational numbers, ratios, rectangles, right triangles, probability, equilateral triangles, and orthocenters. GeoGebra commands used are: OrthogonalLine, Point, Distance, Intersect, Polygon, Rotate, Segment, Circle, Line, Midpoint, Text, If. Suitable for middle school and above students to understand geometric transformations and ratio calculations.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, xAxis) → f
  2. OrthogonalLine(A, yAxis) → g
  3. Point(f) → B
  4. Distance(A, B) → a
  5. OrthogonalLine(D, g) → h
  6. OrthogonalLine(B, f) → i
  7. Intersect(h, i) → C
  8. Polygon(A, B, C, D) → q1, a_1, b_1, d, c
  9. Rotate(A, (-α), Cent) → A'
  10. Rotate(B, (-α), Cent) → B'
  11. Rotate(C, (-α), Cent) → C'
  12. Rotate(D, (-α), Cent) → D'
  13. Polygon(A', B', C', D') → q1', a', b', c', d'
  14. Segment(A' + (0, 0.2), D' + (0, 0.2)) → j
  15. Segment(D + (0.2, 0), C + (0.2, 0)) → k
  16. Circle(A', 0.2) → e
  17. Circle(D', 0.2) → p
  18. Circle(C', 0.2) → q
  19. Line(B', A') → l
  20. Line(A', D') → m
  21. Line(D', C') → n
  22. Circle(A', 0.2) → s
  23. Circle(D', 0.2) → t
  24. Circle(C', 0.2) → c_1
  25. Line(B', C') → f_1
  26. Intersect(s, l, 2) → E
  27. Intersect(t, n, 1) → F
  28. Segment(E, F) → g_1
  29. Intersect(t, m, 2) → G
  30. Intersect(c_1, f_1, 2) → H
  31. Segment(H, G) → h_1
  32. Midpoint(g_1) → I
  33. Midpoint(h_1) → J
  34. OrthogonalLine(I, g_1) → i_1
  35. OrthogonalLine(J, h_1) → j_1
  36. Circle(I, 0.4) → d_1
  37. Circle(J, 0.2) → e_1
  38. Intersect(d_1, i_1, 2) → K
  39. Intersect(e_1, j_1, 1) → L
  40. Text(r, K, true, true) → text1
  41. Text("1", L, true, true) → text2
  42. If(α ≟ 0, landtext, If[α ≟ 90°, porttext, ""]) → orienttext

AI Drawing Prompt Reference

Draw a rectangle and rotate it around a point to form two new rectangles. Draw segments and circles on the edges of the new rectangles, find their intersections and connect them to form new segments. Then, find the midpoints of these segments, draw perpendicular lines and find their intersections, and draw additional circles and segments. Finally, add text at specific locations.
The prompt above was compiled from the original drawing commands and is for reference only.