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Rotation Animation Demonstrating Inscribed Angle

Rotation Animation Demonstrating Inscribed Angle
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2016-06-15 21:19
CircleAngleTransformation
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Parallel Lines and Planes Angles in Parallel Line
This example uses rotation animation to demonstrate the properties of inscribed angles. Key mathematical concepts include the relationship between inscribed angles, central angles, and chords. Using GeoGebra commands such as Rotate, Angle, Circle, and Intersect, the dynamic relationship between inscribed angles and central angles is illustrated. Suitable for middle school and above students to learn about circle geometry.

GeoGebra Commands & Parameters

  1. Point(a) → B
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Line(A, B') → b
  5. Circle(A, 1) → e
  6. Intersect(b, d) → C
  7. Circle(C, 1) → f
  8. Intersect(e, a) → D, E
  9. Intersect(e, b) → F, G
  10. Intersect(f, b) → H, I
  11. Intersect(f, d) → J, K
  12. CircleSector(C, J, H) → k
  13. CircleSector(C, H, K) → p
  14. CircleSector(A, E, G) → q
  15. CircleSector(A, G, D) → r
  16. CircleSector(A, F, E) → t
  17. Dilate(A, If[0 < i < 1, 1 - i], C) → A'
  18. Vector(A, A') → u
  19. Translate(q, u) → q'
  20. Translate(r, u) → r'
  21. Translate(t, u) → t'
  22. CircleArc(A, E, G) → c_1
  23. CircleArc(A, G, D) → f_1
  24. CircleArc(C, J, H) → h_1
  25. CircleArc(C, H, K) → p_1
  26. Vector(A, C) → v
  27. Translate(q, v) → q'_1
  28. Rotate(q'_1, (((-(i - 1)) * 180))°, C) → g
  29. Translate(r, v) → r'_1
  30. Rotate(r'_1, (((i - 1) * 180))°, C) → h