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Median on Hypotenuse - Exercises

Median on Hypotenuse - Exercises
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2017-08-31 01:48
TriangleCoordinate GeometryGeometric Construction
In collections Right Triangle Properties
This example demonstrates the properties and construction of the median on the hypotenuse of a right triangle. It involves core mathematical concepts such as the median theorem, vectors, rotation, and coordinate geometry. Key GeoGebra commands used include Segment, Midpoint, Angle, OrthogonalLine, Rotate, Ray, and Intersect to construct the figure, with interactive buttons to illustrate the median's characteristics. Suitable for high school mathematics teaching or student exploration of geometric properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Midpoint(h) → D
  5. Segment(B, D) → i
  6. Angle(C, B, A) → α
  7. Segment(A, D) → j
  8. Segment(D, C) → k
  9. Segment(E, F) → l
  10. Segment(F, G) → m
  11. Segment(E, G) → p
  12. Midpoint(p) → H
  13. Segment(F, H) → q
  14. Segment(E, H) → r
  15. Angle(E, F, G) → β
  16. Segment(I, J) → s
  17. OrthogonalLine(I, s) → t
  18. Rotate(I, (-(30°)), J) → I'
  19. Angle(I', J, I) → γ
  20. Ray(J, I') → d_1
  21. Intersect(t, d_1) → K
  22. Segment(I, K) → e
  23. Segment(K, J) → d
  24. Angle(J, I, K) → δ
  25. Midpoint(d) → L
  26. Segment(I, L) → f_1
  27. Segment(K, L) → g_1
  28. Segment(J, L) → h_1