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Rectangle, Rhombus, Square by Stephen Greene

Rectangle, Rhombus, Square by Stephen Greene
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2016-11-15 02:33
PolygonTransformationGeometric Construction
This example demonstrates the geometric properties of rectangles, rhombuses, and squares. Key mathematical concepts include geometric transformations, straight lines, and polygons. Using GeoGebra commands such as Segment, OrthogonalLine, and Polygon, these shapes can be constructed and their properties explored. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. Point(g) → D
  5. OrthogonalLine(D, g) → i
  6. Intersect(h, i) → C
  7. Polygon(A, B, C, D) → poly1, a, b, d, c
  8. Segment(F, G) → j
  9. Circle(F, G) → e
  10. Point(e) → I
  11. LineBisector(G, I) → k
  12. Circle(G, F) → p
  13. Intersect(p, k, 2) → H
  14. Polygon(G, H, I, F) → poly2, f_1, h_1, g_1, e_1
  15. Polygon(L, K, 4) → poly3, l, m, n, q, N, M
  16. Segment(A, C) → r
  17. Segment(B, D) → s
  18. Segment(F, H) → t
  19. Segment(G, I) → i_1
  20. Segment(M, K) → j_1
  21. Segment(N, L) → k_1
  22. Intersect(r, s) → E
  23. Intersect(j_1, k_1) → O
  24. Intersect(t, i_1) → O_1
  25. Angle(B, E, A) → α
  26. Angle(G, O_1, F) → β
  27. Angle(L, O, K) → γ
  28. Perimeter(poly1) → perimeterpoly1
  29. PointIn(poly1) → Pointpoly1_1
  30. Distance(A, C) → distanceAC
  31. Midpoint(A, C) →
  32. Perimeter(poly1) → o
  33. PointIn(poly1) → Pointpoly1
  34. Distance(B, D) → distanceBD
  35. Midpoint(B, D) →
  36. Distance(F, H) → distanceFH
  37. Midpoint(F, H) →
  38. Distance(G, I) → distanceGI
  39. Midpoint(G, I) →
  40. Perimeter(poly2) → perimeterpoly2
  41. PointIn(poly2) → Pointpoly2
  42. Distance(K, M) → distanceKM
  43. Midpoint(K, M) →
  44. Distance(L, N) → distanceLN
  45. Midpoint(L, N) →

AI Drawing Prompt Reference

Draw a rectangle, a rhombus, and a square to demonstrate their geometric properties. Start by drawing a line segment and perpendicular lines from its endpoints to create the rectangle. Then, draw two line segments to form the rhombus and square using their intersection points and endpoints. Label the side lengths and perimeters. Finally, draw line segments connecting the diagonals of the rectangle and rhombus, marking their intersections and angles.
The prompt above was compiled from the original drawing commands and is for reference only.