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Triangle Angle Sum Animation

Triangle Angle Sum Animation
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2015-10-20 14:42
TriangleAngleGeometric Construction
This example visually demonstrates that the sum of the interior angles of a triangle is always 180° through animation. It involves core math concepts like triangle angles, geometric proof, and properties of parallel lines. Constructed using GeoGebra commands such as Polygon, Midpoint, Segment, OrthogonalLine, Intersect, Mirror, and Angle to create the triangle and auxiliary lines, showcasing angle changes dynamically. Suitable for middle school students and above for learning geometric theorem proofs and for educational demonstrations.

GeoGebra Commands & Parameters

  1. Polygon(C, B, A) → poly1, a, c, b
  2. Midpoint(a) → D
  3. Midpoint(c) → E
  4. Segment(D, E) → d
  5. OrthogonalLine(D, b) → f
  6. OrthogonalLine(E, b) → g
  7. Intersect(f, b) → F
  8. Intersect(g, b) → G
  9. Segment(F, D) → f'
  10. Segment(G, E) → g'
  11. Mirror(B, d) → B'
  12. Segment(B, B') → h
  13. Polygon(E, D, B'') → poly2, b_2, e_2, d_2
  14. Polygon(G, E, A'') → poly3, a_3, g_3, e_3
  15. Polygon(F, D, C'') → poly4, c_4, f_4, d_4
  16. Polygon(E, D, B) → poly5, b_5, e_5, d_5
  17. Polygon(G, E, A) → poly6, a_6, g_6, e_6
  18. Polygon(F, D, C) → poly7, c_7, f_7, d_7
  19. Angle(E, B'', D) → β
  20. Angle(E, B, D) → β_1
  21. Angle(G, A'', E) → α
  22. Angle(G, A, E) → α_1
  23. Angle(D, C'', F) → γ
  24. Angle(D, C, F) → γ_1