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Perpendicular Vectors in a 3:4:5 Similar Triangle

Perpendicular Vectors in a 3:4:5 Similar Triangle
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2019-10-13 20:30
TriangleVectorCoordinate Geometry
This example demonstrates perpendicular vectors in a 3:4:5 similar triangle. Key mathematical concepts include vectors and similar triangles. Using GeoGebra commands such as Intersect, Line, Point, and Vector, perpendicular vectors can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and vector topics.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Line(O, A) → f
  3. Point(f) → Fm
  4. Vector(O, Fm) → F
  5. Length(F) → lF
  6. Point(F) → D
  7. Line(D, xAxis) → g
  8. Point(F) → E
  9. Line(E, yAxis) → h
  10. Intersect(g, h) → G
  11. Polygon(D, E, G) → t1, g_1, d, e
  12. Angle(G, D, E) → θ
  13. Line(Fm, yAxis) → i
  14. Line(Fm, xAxis) → j
  15. Intersect(j, yAxis) → H
  16. Intersect(i, xAxis) → I
  17. Vector(O, I) → Fx
  18. Vector(O, H) → Fy
  19. Segment(H, Fm) → k
  20. Segment(Fm, I) → l
  21. Angle(I, O, Fm) → α
  22. OrthogonalLine(O, f) → m
  23. Intersect(m, j) → B
  24. Vector(O, B) → u
  25. Point(u) → C
  26. Point(u) → J
  27. Line(C, yAxis) → n
  28. Line(C, xAxis) → p
  29. Line(J, yAxis) → q
  30. Intersect(p, q) → K
  31. Polygon(C, K, J) → t2, j_1, c, k_1
  32. Angle(Fm, O, B) → β
  33. Angle(K, J, C) → γ
  34. Line(B, yAxis) → r
  35. Intersect(xAxis, r) → L
  36. Vector(O, L) → v
  37. Line(B, xAxis) → s
  38. Vector(L, B) → w

AI Drawing Prompt Reference

Draw a 3:4:5 similar triangle and construct two perpendicular vectors within it. Start by drawing the intersection point O of the x-axis and y-axis, then draw a line f through O parallel to the x-axis, and take point Fm on f to construct vector F. Next, draw the length lF of F and take point D on F, draw a line g through D parallel to the x-axis, and take point E on g to draw a line h parallel to the y-axis, with their intersection point G. Construct triangle DEG. Then, draw a line m perpendicular to f, intersecting the y-axis at point B, construct vector u, and take point C on u, draw a line n parallel to the y-axis through C, and take point K on n to construct triangle CKJ. Finally, draw a line r perpendicular to B, intersecting the x-axis at point L, and construct vector v.
The prompt above was compiled from the original drawing commands and is for reference only.