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Median Line of a Triangle

Median Line of a Triangle
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2015-10-07 16:39
TriangleVectorGeometric Construction
This example demonstrates the median line of a triangle, which is a line segment connecting a vertex to the midpoint of the opposite side. Key mathematical concepts include triangles, segments, area, and geometric transformations. Using GeoGebra commands such as Polygon, Segment, Circle, Intersect, Line, Vector, Rotate, etc., a dynamic model of a triangle's median line is constructed. Suitable for middle school and above students to learn geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → Vieleck1, c, a, b
  2. Segment(A, C) → d
  3. Circle(A, (sqrt(2) * d / 2)) → e
  4. Circle(C, (sqrt(2) * d / 2)) → f
  5. Intersect(f, e) → D, E, ,
  6. Line(E, D) → g
  7. Intersect(g, b) → M
  8. Line(B, M) → h
  9. Vector(J, K) → u
  10. Rotate(E, -15*°, C) → E'
  11. Angle(E', C, E) → α
  12. Mirror(E', b) → E''
  13. CircleArc(C, E', E'') → k
  14. Mirror(E', g) → E''_1
  15. Mirror(E''_1, b) → F
  16. CircleArc(A, F, E''_1) → p
  17. Circle(M, C) → q
  18. Intersect(q, h, 2) → G
  19. Vector(H, I) → v
  20. Vector(L, N) → w
  21. Vector(O, P) → j

AI Drawing Prompt Reference

Draw a triangle ABC, then draw the median line AM from vertex A to the midpoint M of side BC. Draw an arc centered at A with AM as radius, and another arc centered at C with CM as radius, which intersect at points E and E'. Draw a line segment from E to E', then rotate E' to E''. Draw an arc centered at C with E'' as radius. Draw another arc centered at M with E'' as radius, which intersects BC at F. Draw an arc centered at F with E'' as radius, which intersects AM at G. Finally, draw an arc centered at M with G as radius, which intersects BC at H.
The prompt above was compiled from the original drawing commands and is for reference only.