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Rectangle, Rhombus, and Square

Rectangle, Rhombus, and Square
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2018-02-13 01:15
CirclePolygonGeometric Construction
This example demonstrates the properties and relationships of rectangles, rhombuses, and squares. It involves core mathematical concepts such as polygons, angles, equations, ratios, variance, indefinite integral, and circumcircle. The construction uses GeoGebra commands like Segment, OrthogonalLine, Point, Intersect, Polygon, Circle, AngularBisector, Rotate, Distance, and Angle. It is suitable for high school mathematics teaching or exploration by geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. Point(g) → C
  4. OrthogonalLine(C, g) → h
  5. OrthogonalLine(B, f) → i
  6. Intersect(h, i) → D
  7. Polygon(A, C, D, B) → q1, a, c, d, b
  8. Segment(E, F) → j
  9. Circle(E, F) → e
  10. Point(e) → G
  11. Segment(E, G) → k
  12. Segment(G, F) → l
  13. AngularBisector(F, E, G) → m
  14. Circle(F, E) → p
  15. Intersect(p, m, 2) → H
  16. Polygon(E, F, H, G) → q2, e_1, f_1, h_1, g_1
  17. Segment(E, H) → n
  18. Segment(C, B) → q
  19. Segment(D, A) → r
  20. Segment(I, J) → s
  21. Rotate(J, 90°, I) → L
  22. Rotate(I, 90°, L) → K
  23. Polygon(I, L, K, J) → q3, i_1, j', i', j_1
  24. Segment(I, K) → t
  25. Segment(J, L) → k_1
  26. Distance(C, B) → distanceCB
  27. Distance(A, D) → distanceAD
  28. Intersect(l, n) → M
  29. Angle(H, M, F) → α

AI Drawing Prompt Reference

Draw a rectangle, a rhombus, and a square to demonstrate their relationships. Start by drawing a line segment, then find a point on a perpendicular line above it, and draw another perpendicular line from this point to intersect with the first perpendicular line, forming a rectangle. Next, draw a circle and take a point on it to create a rhombus by connecting the points. Finally, rotate the rhombus by 90 degrees to form a square, highlighting their geometric properties.
The prompt above was compiled from the original drawing commands and is for reference only.