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Coordinate Geometry Parallelogram Construction and Proof

Coordinate Geometry Parallelogram Construction and Proof
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2016-05-29 14:05
PolygonVectorCoordinate GeometryGeometric Construction
In collections Expressing Geometric Properties with Equations (GPE) Cluster Unit 7: Polygons and Quadrilaterals Coordinate Geometry Proof Prompts
This example demonstrates the construction and proof of a parallelogram using coordinate geometry. It involves core concepts like coordinate geometry, vectors, angles, and polygon construction. GeoGebra commands and objects used include Ray, Point, Distance, Circle, Intersect, Polygon, OrthogonalLine, Dilate, Angle, Vector, and Segment. Suitable for high school mathematics teaching, focusing on coordinate geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Point(f) → C
  3. Ray(A, D) → g
  4. Point(g) → E
  5. Point(h) → F
  6. Ray(E, F) → i
  7. Ray(E, F) → j
  8. Point(j) → G
  9. Distance(A, C) → a
  10. Circle(G, a) → c
  11. Intersect(c, j) → H, I
  12. Polygon(A, C, H, G) → poly1, a_1, c_1, h_1, g_1
  13. OrthogonalLine(G, k) → l
  14. Intersect(k, xAxis) → J
  15. Intersect(l, k) → K
  16. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], K) → A'
  17. Angle(G, K, A) → α
  18. Vector(A, A') → u
  19. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], E) → A'_1
  20. Dilate(K, If[1 < b ≤ 2, 2 - b, 0], G) → K'
  21. Vector(K, K') → v
  22. Vector(A, A'_1) → w
  23. Segment(A, C) → m
  24. Segment(C, H) → n
  25. Segment(H, G) → p
  26. Segment(G, A) → q