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Similar Triangles in Cartesian Coordinate System

Similar Triangles in Cartesian Coordinate System
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2019-09-19 19:15
TriangleVectorCoordinate GeometryOptimizationGeometric Construction
This example demonstrates how to construct similar triangles in a Cartesian coordinate system. It involves core mathematical concepts such as triangle similarity criteria, vector operations, linear programming or optimization, and matrix transformations. Key GeoGebra commands and objects used in the construction include Polygon, Vector, Textfield, Segment, Rotate, Intersect, and Angle, as outlined in the construction summary. It is suitable for high school and above students learning about coordinate geometry, similarity, and transformations.

GeoGebra Commands & Parameters

  1. Polygon((wl, wd), (wr, wd), (wr, wu), (wl, wu)) → wn, wnd, wnr, wnu, wnl
  2. Vector((wl, 0), (wr, 0)) → xaxis
  3. Vector((0, wd), (0, wu)) → yaxis
  4. Textfield(k) → InputBox1
  5. Textfield(d) → InputBox2
  6. Segment(O, A) → sOA
  7. Rotate(A, ((-π)) / 2, B) → C
  8. Segment(A, B) → sAB
  9. Segment(C, D) → sCD
  10. Segment(B, C) → sBC
  11. Segment(D, A) → sDA
  12. Intersect(sCD, Line[O, P]) → M
  13. Segment(O, M) → sOM
  14. Intersect(sAB, Line[O, M]) → N
  15. Polygon(D, R, M) → plDRM, m, d_1, r
  16. Polygon(A, O, N) → plAON, n, a_1, o
  17. Angle(A, N, O) → aANO
  18. Angle(D, M, R) → aDMR