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Cyclic Quadrilateral Quick Warm Up

Cyclic Quadrilateral Quick Warm Up
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2018-06-06 10:18
CirclePolygonAngleGeometric Construction
This example demonstrates properties and criteria of cyclic quadrilaterals. Key math concepts include circle properties, sum of interior angles of quadrilaterals, and supplementary opposite angles. Construction highlights involve GeoGebra commands like Circle, Point, Polygon, Segment, Ray, Min, Intersect, Angle, Rotate, CircleSector, Dilate, Vector, Translate, and Line. Suitable for high school students exploring geometric properties and construction techniques.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. CircleArc(A, C, D) → d
  5. CircleArc(A, D, C) → e
  6. Point(e) → E
  7. CircleArc(A, D, E) → f
  8. CircleArc(A, E, C) → g
  9. Point(g) → F
  10. Polygon(F, C, D, E) → q1, f_1, c_1, d_1, e_1
  11. Segment(C, D) → h
  12. Segment(D, E) → i
  13. Segment(E, F) → j
  14. Ray(F, C) → k
  15. Min({i, j, h, Distance[F, C]}) → a
  16. Circle(E, (0.25 * a)) → p
  17. Intersect(p, j) → G,
  18. Angle(F, E, D) → α
  19. Rotate(G, If[0 < b ≤ 1, (b * α), α], E) → G'
  20. CircleSector(E, G, G') → q
  21. Dilate(E, If[1.5 < b ≤ 2.5, 2.5 - b, 0], C) → E'
  22. Vector(E, E') → u
  23. Translate(q, u) → q'
  24. Line(E, k) → l
  25. Point(l) → H
  26. Angle(G, E, H) → β
  27. Rotate(q', If[1.5 < b ≤ 2.5, ((b - 1.5) * β), β], E') → q''