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How to Copy a Line Segment with a Collapsing Compass

How to Copy a Line Segment with a Collapsing Compass
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2016-11-22 19:41
TriangleCircleGeometric Construction
This example demonstrates the geometric construction of copying a line segment using a collapsing compass. Key math concepts involved include line segments, intersections, similar triangles, and geometric construction. The construction utilizes GeoGebra commands and objects such as Circle, Intersect, Ray, Segment, and Point. Suitable for middle school and above students learning geometric constructions.

GeoGebra Commands & Parameters

  1. Circle(B, C) → e
  2. Circle(A, B) → d
  3. Circle(B, A) → c
  4. Intersect(c, d, 1) → O
  5. Ray(O, B) → g
  6. Intersect(e, g, 2) → D
  7. Intersect(e, g, 1) → E
  8. Segment(B, C) → f
  9. Circle(O, If[Defined[D], D, E]) → k
  10. Ray(O, A) → h
  11. Intersect(k, h, 1) → L
  12. Intersect(k, h, 2) → F
  13. Intersect(c, d, 2) → G
  14. Ray(G, B) → j
  15. Intersect(e, j, 2) → H
  16. Circle(A, L) → p
  17. Point(p) → I
  18. Segment(A, I) → i

AI Drawing Prompt Reference

Draw a line segment and two circles with different centers, intersecting to find a point. From this point, draw a ray and let it intersect the circles to get two points. Connect these points to form a line segment. Then, draw another circle with a different center and intersect it with the ray to get two points. Connect these points to form another line segment. Finally, draw a circle with one of the points as the center and intersect it with the ray to get a point. Connect this point to the other point to complete the construction.
The prompt above was compiled from the original drawing commands and is for reference only.