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Construct a Square by Its Diagonal

Construct a Square by Its Diagonal
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2019-05-06 01:20
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to construct a square using its diagonal. Key mathematical concepts include geometric construction, symmetry, and continuity. Using GeoGebra commands such as Segment, JednakoudaljenaTačka, Line, Intersect, Circle, and Polygon, a square can be constructed. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. JednakoudaljenaTačka(A, B) → c, d, C
  3. JednakoudaljenaTačka(B, A) → e, g, D
  4. Line(C, D) → h
  5. Intersect(h, f) → S
  6. Circle(S, A) → k
  7. Intersect(k, h, 1) → E
  8. Polygon(A, E, 4) → poligon1, i, j, l, m, F, G

AI Drawing Prompt Reference

Draw a square given its diagonal. Start by drawing the diagonal AB, then find the midpoints C and D of AB, and draw a line through C and D, intersecting AB at point S. With S as the center and SA as the radius, draw a circle, which intersects the line at point E. Finally, connect points A, E, and the endpoints of the diagonal to form the square.
The prompt above was compiled from the original drawing commands and is for reference only.