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W24/4 Division of a Segment by a Given Ratio

W24/4 Division of a Segment by a Given Ratio
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2020-11-13 05:05
Geometric ConstructionSlider Animation
① This example demonstrates how to divide a line segment into a given ratio using geometric construction, with the dividing point dynamically updating as the ratio changes. ② Core mathematical concepts include proportional division of segments, similar triangles, and the use of circles and perpendicular lines to construct the division point, emphasizing ratio relationships and geometric construction. ③ Construction highlights: Based on the construction summary, GeoGebra commands such as Segment, Point, Circle, OrthogonalLine, Intersect, CircleArc, Angle, and Line are used, creating objects like A, B, C, D, E, F, G, H, I, J, K, along with auxiliary circles and perpendiculars to determine the division point, while angles and text objects label the ratio. ④ Suitable for upper middle school or high school students to understand the geometric construction of segment division by a ratio, and useful for teachers in classroom demonstrations or for student self-exploration to connect proportional division with similar figures.

GeoGebra Commands & Parameters

  1. Segment(C, D) → f
  2. Point(f) → E
  3. Segment(C, E) → h
  4. Circle(E, C) → c
  5. OrthogonalLine(E, f) → g
  6. Circle(E, C) → d
  7. Intersect(d, g, 2) → F
  8. CircleArc(E, F, C) → e
  9. Segment(E, F) → i
  10. Angle(F, E, C) → α
  11. Segment(C, F) → j
  12. Line(C, F) → k
  13. Point(k) → G
  14. Segment(F, G) → l
  15. Circle(F, E) → p
  16. OrthogonalLine(C, l) → m
  17. Point(m) → H
  18. CircleArc(C, E, H) → q
  19. Intersect(q, m, 1) → I
  20. Segment(C, I) → n
  21. Angle(F, C, I) → β
  22. Segment(F, I) → r
  23. Circle(F, I) → s
  24. Intersect(s, l, 1) → J
  25. Segment(F, J) → t
  26. CircleArc(F, J, I) → c_1
  27. Segment(J, D) → a
  28. Line(F, a) → b
  29. Intersect(b, f) → K
  30. Segment(F, K) → f_1

AI Drawing Prompt Reference

Draw a line segment CD and find point E as the midpoint. Use circles and perpendicular lines to construct point F dividing CD in the ratio 1:3. Then, draw a circle with center F and radius FC, and construct line segment EF. Take point G on EF. Draw a circle with center F and radius FG, and construct line segment FG. Take point H on FG. Draw a circle with center F and radius FH, and construct line segment FH. Take point I on FH. Draw a circle with center F and radius FI, and construct line segment FI. Take point J on FI. Finally, connect FJ and find its intersection with CD, which is point K, the division point.
The prompt above was compiled from the original drawing commands and is for reference only.