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Vertically Opposite Angles Demo

Vertically Opposite Angles Demo
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2013-02-21 07:17
AngleGeometric Construction
In collections Introduction to Geometry
This example demonstrates how vertically opposite angles are formed and their properties through an interactive applet. The core math concept involved is the equality of vertically opposite angles. Construction highlights include using GeoGebra commands/objects: Circle, Point, Line, Rotate, Angle, Segment, Intersect, Midpoint. Suitable for middle school students learning about angle concepts.

GeoGebra Commands & Parameters

  1. Circle(E, 3) → e
  2. Point(e) → A
  3. Line(A, E) → c
  4. Point(c) → C
  5. Rotate(A, β_1, E) → B
  6. Line(B, E) → d
  7. Point(d) → D
  8. Angle(A, E, B) → β
  9. Angle(C, E, D) → α
  10. Angle(B, E, C) → γ
  11. Angle(D, E, A) → δ
  12. Segment(B, D) → b
  13. Segment(A, C) → a
  14. Circle(E, 1.5) → f
  15. Intersect(f, a, 1) → G
  16. Intersect(f, b, 2) → H
  17. Intersect(f, a, 2) → I
  18. Intersect(f, b, 1) → J
  19. Midpoint(J, G) → K
  20. Midpoint(G, H) → L
  21. Midpoint(H, I) → M
  22. Midpoint(I, J) → N
  23. Line(L, N) → g
  24. Line(K, M) → h
  25. Intersect(f, g, 1) → F
  26. Intersect(f, g, 2) → P
  27. Intersect(f, h, 2) → Q
  28. Intersect(f, h, 1) → R

AI Drawing Prompt Reference

Draw a circle e, then take points A and C on the circle, draw line c through A and E, rotate A to get B, draw line d through B and E, then draw angles ∠AEB, ∠CED, ∠CEB, and ∠DEA, connect BD and AC, draw circle f, and find intersections G, H, I, J with AC and BD, take midpoints K, L, M, N of GJ, GH, HI, IJ, draw lines KL and MN, and find intersections F, P, Q, R with circle f.
The prompt above was compiled from the original drawing commands and is for reference only.