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Orthocenter of a Triangle by nicoleshibata

Orthocenter of a Triangle by nicoleshibata
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2019-12-11 03:15
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 Polygon, Midpoint, Segment, Intersect, and OrthogonalLine, a triangle can be constructed and its orthocenter found. Suitable for middle school and above students to learn triangle geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Midpoint(C, B) → D
  3. Midpoint(C, A) → E
  4. Midpoint(B, A) → F
  5. Segment(C, F) → f
  6. Segment(B, E) → g
  7. Segment(A, D) → h
  8. Intersect(f, g) → G
  9. OrthogonalLine(C, c) → i
  10. OrthogonalLine(A, a) → j
  11. OrthogonalLine(B, b) → k
  12. Intersect(i, j) → orthocenter

AI Drawing Prompt Reference

Draw a triangle with three vertices. Mark the midpoint of each side. Connect each vertex to the midpoint of the opposite side to form three medians, which intersect at one point. Then, from each vertex, draw a line perpendicular to the opposite side to form three altitudes. These altitudes intersect at a single point, which is the orthocenter. Use distinct colors for medians and altitudes, and clearly label the orthocenter.
The prompt above was compiled from the original drawing commands and is for reference only.