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Heights in Triangles

Heights in Triangles
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2019-02-21 20:46
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the heights in triangles. Key mathematical concepts include triangle heights, perpendicular lines, and polygons. Using GeoGebra commands such as Segment, Point, Line, Intersect, OrthogonalLine, and Polygon, one can construct triangles and their heights. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h_4
  4. Point(h_4) → D
  5. Line(D, f) → i
  6. Intersect(i, g) → E_1
  7. Segment(E_1, B) → j
  8. Point(j) → F_1
  9. Line(F_1, h_4) → k
  10. Intersect(k, f) → E
  11. Intersect(i, k) → F
  12. Line(C, B) → l
  13. OrthogonalLine(A, l) → m
  14. Intersect(l, m) → G
  15. Segment(A, G) → h
  16. OrthogonalLine(D, l) → n
  17. Intersect(l, n) → H
  18. Segment(D, H) → h_1
  19. OrthogonalLine(F, l) → p
  20. Intersect(p, l) → I
  21. Segment(F, I) → h_2
  22. OrthogonalLine(E, l) → q
  23. Intersect(q, l) → J
  24. Segment(E, J) → h_3
  25. Segment(E, F) → r
  26. Segment(D, F) → s
  27. Polygon(D, E_1, C) → t1, c, d, e_1
  28. Polygon(E_1, F_1, F) → t2, f_1, e_2, f_2
  29. Polygon(E, B, F_1) → t3, f_3, e, b

AI Drawing Prompt Reference

Draw a triangle ABC, then draw its three altitudes and mark their intersections as D, E, and F. Next, draw the medians and perpendicular bisectors of the triangle. Finally, use these lines and points to construct three new triangles.
The prompt above was compiled from the original drawing commands and is for reference only.