Orthocenter of a Triangle by hrawson20

Orthocenter of a Triangle by hrawson20
Loading the math board and drawing, please wait…
2016-10-18 08:40
This example demonstrates how to construct the orthocenter of a triangle using GeoGebra, which is the intersection point of the three altitudes. Key math concepts include perpendicular lines, angles, triangle altitudes, intersection points, etc. Construction highlights involve commands like Segment, Circle, Intersect, Point, Line, and Angle to draw sides, circumcircles, feet of altitudes, altitude lines, and measure angles. Suitable for middle school students and above to learn geometric constructions and understand properties of the orthocenter and related theorems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Circle(B, Segment[B, C]) → c
  5. Intersect(c, h, 2) → D
  6. Circle(C, Segment[B, C]) → d
  7. Intersect(d, f, 1) → E
  8. Point(f) → F
  9. Circle(B, Segment[F, B]) → e
  10. Circle(E, Segment[F, B]) → k
  11. Intersect(e, k, 1) → G
  12. Line(G, C) → i
  13. Intersect(i, f) → H
  14. Angle(C, H, F) → α
  15. Point(h) → I
  16. Circle(C, Segment[C, I]) → p
  17. Circle(D, Segment[I, C]) → q
  18. Intersect(p, q, 2) → J
  19. Line(J, B) → j
  20. Intersect(j, h) → K
  21. Angle(B, K, C) → β
  22. Intersect(i, j) → L