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Parallelogram and Vector Demonstration

Parallelogram and Vector Demonstration
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2016-07-27 09:23
VectorCoordinate GeometryGeometric Construction
In collections Triangle Congruence - Collection
This example demonstrates how to construct a parallelogram using points and vectors, showcasing the properties of its diagonals. Core mathematical concepts include vectors, parallelograms, geometric construction, and coordinate geometry. Construction highlights involve commands/objects like Segment, Circle, Ray, Intersect, Polygon, Angle, Line, and Rotate from GeoGebra. Suitable for high school students to learn vector operations, geometric transformations, and properties of parallelograms, ideal for classroom instruction or self-study.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(C, A) → c
  3. Circle(A, B) → d
  4. Ray(C, B) → b
  5. Intersect(d, b, 2) → D
  6. Segment(A, D) → e
  7. Segment(B, C) → f
  8. Polygon(A, D, C) → poly1, c_1, a_1, d_1
  9. Polygon(A, B, C) → poly2, c_2, a_2, b_1
  10. Angle(A, C, B) → α
  11. Line(E, g) → h
  12. Rotate(h, (-α), E) → h'
  13. Circle(E, b_1) → k
  14. Intersect(k, h', 1) → F
  15. Circle(E, a_2) → p
  16. Intersect(p, h, 1) → G
  17. Line(H, g) → i
  18. Rotate(i, (-α), H) → i'
  19. Circle(H, If[Defined[D], d_1]) → q
  20. Intersect(q, i', 1) → I
  21. Circle(H, a_1) → r
  22. Intersect(r, i, 1) → J
  23. Polygon(H, I, J) → poly3, j, h_1, i_1
  24. Polygon(E, F, G) → poly4, g_1, e_1, f_1
  25. Angle(F, E, G) → β
  26. Angle(I, H, J) → γ