MathPlotAI Logo MathPlotAI

Guess the Orthocenter!

Guess the Orthocenter!
Loading the math board and drawing, please wait…
2020-05-08 22:14
TriangleAngleVectorCoordinate GeometryGeometric Construction
This example demonstrates how to estimate the orthocenter of a triangle through interactive means. Key math concepts involved include the orthocenter, triangle geometry, vectors, and reflections. Construction highlights from the GeoGebra command summary involve commands like Random, Circle, Rotate, Ray, Intersect, Line, OrthogonalLine, Segment, Polygon, Distance, Midpoint, If, and objects such as t2, A, c, d, etc. It is suitable for high school mathematics education as a quick formative assessment tool to gauge students' understanding of orthocenter properties.

GeoGebra Commands & Parameters

  1. Random(2, 6) → c
  2. Circle(A, c) → d
  3. Random(30, 150) → a
  4. Random(2, 6) → b
  5. Rotate(B, (a * π / 180), A) → B'
  6. Ray(A, B') → g
  7. Intersect(d, g, 1) → C
  8. Line(C, B) → n
  9. OrthogonalLine(A, n) → p
  10. Line(A, C) → m
  11. OrthogonalLine(B, m) → q
  12. Intersect(p, q) → E
  13. Segment((0, 0), (b, 0)) → f
  14. Polygon(A, B, C) → t1_1, c_1, a_1, b_1
  15. Distance(E, t2) → e
  16. Midpoint(b_1) → F
  17. Midpoint(a_1) → G
  18. Midpoint(f) → H
  19. If(e ≤ 0.2, "Nice job!", 0.2 < e ≤ 1, "Pretty good!", "Not quite.") → text2
  20. Line(A, B) → l
  21. OrthogonalLine(C, l) → r
  22. Intersect(l, r) → I
  23. Angle(B, I, C) → α
  24. Intersect(m, q) → J
  25. Angle(A, J, B) → γ
  26. Intersect(n, p) → K
  27. Angle(A, K, C) → β