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Symmetry and 3D Vectors

Symmetry and 3D Vectors
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2017-10-03 21:45
VectorSolid GeometryGeometric Construction
This example demonstrates the relationship between symmetry and vectors in three-dimensional space. It involves core mathematical concepts such as symmetry, 3D vectors, incircle, Pythagorean theorem, and scalene triangles. The construction uses GeoGebra commands like Circle, Point, Segment, LineBisector, Intersect, Angle, Textfield, and CircumcircleArc. It is suitable for high school and above students studying spatial geometry and vector applications.

GeoGebra Commands & Parameters

  1. Circle(O, X) → c
  2. Point(c) → B
  3. Point(c) → A
  4. Segment(A, B) → AB
  5. Point(c) → D
  6. Point(c) → C
  7. Segment(C, D) → CD
  8. LineBisector(AB) → d
  9. LineBisector(CD) → e
  10. Intersect(e, CD) → Q
  11. Intersect(d, AB) → P
  12. Segment(Q, O) → f
  13. Segment(O, P) → g
  14. Angle(O, Q, D) → α
  15. Textfield() → inputBox2
  16. Circle(O_1, X_1) → c_1
  17. Point(c_1) → A_1
  18. Point(c_1) → B_1
  19. Point(AB) → E
  20. Point(CD) → F
  21. Point(c) → I
  22. Point(c) → J
  23. CircumcircleArc(C, I, J) → k
  24. Point(c) → G
  25. CircumcircleArc(B, G, A) → h
  26. Angle(O, P, B) → β