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Exercise 2.14 - Quick Segment Trisection

Exercise 2.14 - Quick Segment Trisection
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2020-04-08 01:15
Coordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates how to quickly trisect a segment. Key mathematical concepts include geometric construction and coordinate geometry. It uses commands such as Segment, Circle, Intersect, Line, Midpoint, and Polygon in GeoGebra. Suitable for middle school and above students to learn geometric construction techniques.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Circle(A, B) → c
  3. Circle(B, A) → d
  4. Intersect(c, d) → C, D, ,
  5. Circle(C, B) → e
  6. Line(B, C) → b
  7. Intersect(e, b) → E_1, E
  8. Line(E, D) → f
  9. Intersect(f, a) → F
  10. Circle(F, A) → g
  11. Intersect(g, a) → H, G
  12. Midpoint(A, B) → M
  13. Polygon(E, A, B) → t1, b_1, e_2, a_2
  14. Polygon(C, M, B) → t2, b_2, c_1, m_1
  15. Polygon(E, A, F) → poly1, f_1, e_1, a_1
  16. Polygon(F, D, M) → poly2, m, f_2, d_1

AI Drawing Prompt Reference

Draw a line segment AB, then draw two circles with A and B as diameters, find their intersection points C and D. Draw a circle centered at C, intersecting AB at E. Draw line segment BC, find its intersection with the new circle at F. Draw a circle centered at F, intersecting AB at G and H. Find the midpoint M of AB. Draw triangles EAB, CMB, EAF, and FDM.
The prompt above was compiled from the original drawing commands and is for reference only.