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Construction of a Square (Step-by-Step)

Construction of a Square (Step-by-Step)
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2019-02-10 05:11
CirclePolygonCoordinate GeometryGeometric Construction
① This example demonstrates how to construct a square step-by-step using only compass and straightedge (ruler) operations, showing the complete geometric construction process. ② The core mathematical concepts include the basic postulates of geometric construction (drawing rays, circles, finding intersections, connecting segments), the definition and properties of a square, and the feasibility of straightedge-and-compass constructions. ③ Construction highlights: from the construction summary, the GeoGebra commands used are Ray, Circle, Intersect, Segment, CircleArc, and Point; objects include text1, A, B_1, f, c, B, g, d, C_1, D_1, e, h, E, F, k, p, G, H, q, I, J, i, r, K, L, s, C, j, t, M, N, c_1, O, P, d_1, D, R, l, m. The construction proceeds by drawing circles and connecting points to determine the four vertices of the square. ④ It is suitable for middle school geometry teaching, introductory geometric construction practice, and for teachers to demonstrate the logical steps of geometric construction, helping students understand the dependency relationships among geometric objects.

GeoGebra Commands & Parameters

  1. Ray(A, B_1) → f
  2. Circle(A, 5) → c
  3. Intersect(c, f) → B,
  4. Segment(A, B) → g
  5. Circle(B, 1) → d
  6. Intersect(d, f) → C_1, D_1
  7. CircleArc(B, D_1, C_1) → e
  8. Circle(D_1, 2) → h
  9. Point(h) → E
  10. Point(h) → F
  11. CircleArc(D_1, E, F) → k
  12. Circle(C_1, 2) → p
  13. Point(p) → G
  14. Point(p) → H
  15. CircleArc(C_1, G, H) → q
  16. Intersect(h, p) → I, J, ,
  17. Ray(B, J) → i
  18. Circle(B, 5) → r
  19. Point(r) → K
  20. Point(r) → L
  21. CircleArc(B, K, L) → s
  22. Intersect(r, i) → C,
  23. Segment(B, C) → j
  24. Circle(C, 5) → t
  25. Point(t) → M
  26. Point(t) → N
  27. CircleArc(C, M, N) → c_1
  28. Point(c) → O
  29. Point(c) → P
  30. CircleArc(A, O, P) → d_1
  31. Intersect(c, t) → D, R, ,
  32. Segment(C, D) → l
  33. Segment(D, A) → m

AI Drawing Prompt Reference

Draw a square by first drawing a ray from point A to B1, then drawing a circle centered at A that intersects the ray at point B. Next, draw a circle centered at B that intersects the ray at points C1 and D1. Connect B to C1, C1 to D1, and D1 to B to form the four sides of the square.
The prompt above was compiled from the original drawing commands and is for reference only.