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Orthocenter of a Triangle by kmacken20

Orthocenter of a Triangle by kmacken20
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2016-10-18 06:23
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the orthocenter of a triangle, which is the point where the three altitudes of a triangle intersect. Using GeoGebra commands such as Segment, Point, Circle, and Intersect, one can construct a triangle and find its orthocenter. Suitable for students at the middle school level and above.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Segment(C_1, A_1) → h_1
  5. Segment(A_2, B_1) → f_1
  6. Point(f_1) → D_2
  7. Circle(C, Segment[A, C]) → c
  8. Circle(A, Radius[c]) → d
  9. Point(f) → D
  10. Circle(A, Segment[D, A]) → e
  11. Segment(A_4, B_2) → f_2
  12. Point(f_2) → D_3
  13. Circle(A_4, Segment[D_3, A_4]) → e_1
  14. Intersect(e, e_1, 1) → E
  15. Segment(C, E) → i
  16. Point(g) → F
  17. Circle(C, Segment[C, F]) → k
  18. Segment(B_3, C_4) → g_1
  19. Point(g_1) → F_1
  20. Circle(C_4, Segment[C_4, F_1]) → k_1
  21. Intersect(k, k_1, 2) → G
  22. Segment(A, G) → j
  23. Intersect(i, j) → H

AI Drawing Prompt Reference

Draw a triangle and construct the altitudes from each vertex to the opposite side, finding their intersection point, which is the orthocenter. Start by drawing the triangle's sides, then draw the altitude from each vertex, and finally mark the intersection point of these altitudes as the orthocenter.
The prompt above was compiled from the original drawing commands and is for reference only.