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Orthocenter of a Right Triangle by Robert Byng

Orthocenter of a Right Triangle by Robert Byng
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2017-10-18 17:23
TriangleAngleGeometric Construction
This example demonstrates the properties and position of the orthocenter in a right triangle. It involves core mathematical concepts such as orthocenter, right triangle, geometric construction, and similarity transformation. The construction uses commands like Polygon, OrthogonalLine, Intersect, Angle, and Line. It is suitable for high school mathematics education and learning to understand the special characteristics and applications of the orthocenter in right triangles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. OrthogonalLine(A, a) → f
  3. OrthogonalLine(C, c) → g
  4. OrthogonalLine(B, b) → h
  5. Intersect(f, g) → Orthocenter
  6. Intersect(f, a) → E
  7. Angle(Orthocenter, E, C) → γ
  8. Line(A, B) → i
  9. Intersect(g, i) → D
  10. Line(C, B) → j
  11. Intersect(f, j) → K
  12. Angle(A, K, C) → α
  13. Line(A, C) → k
  14. Intersect(h, k) → G
  15. Angle(A, G, B) → β
  16. Angle(C, D, A) → δ