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Triangle Angle Sum Proof

Triangle Angle Sum Proof
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2016-01-08 19:59
TriangleAngleGeometric Construction
This example dynamically demonstrates the triangle angle sum theorem. It involves core concepts like triangles, angles, and geometric transformations. GeoGebra commands used include Polygon, Circle, Intersect, CircleSector, Dilate, Vector, Translate, Midpoint, and Rotate. Suitable for middle school and above to understand geometric theorems and transformation applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Circle(A, 2) → d
  3. Circle(C, Radius[d]) → e
  4. Circle(B, Radius[d]) → f
  5. Intersect(d, c, 1) → D
  6. Intersect(d, b, 1) → E
  7. Intersect(e, b, 1) → F
  8. Intersect(e, a, 1) → G
  9. Intersect(f, a, 1) → H
  10. Intersect(f, c, 1) → I
  11. CircleSector(A, D, E) → g
  12. CircleSector(B, H, I) → h
  13. CircleSector(C, F, G) → k
  14. Dilate(B, If[n < 1, 1 - n, 0], C) → B'
  15. Vector(B, B') → u
  16. Translate(A, u) → A'
  17. Translate(B, u) → B'_1
  18. Translate(C, u) → C'
  19. Polygon(A', B'_1, C') → poly1', c', a', b'_1
  20. Translate(g, u) → g'
  21. Translate(h, u) → h'
  22. Translate(k, u) → k'
  23. Midpoint(b) → J
  24. If(n > 1, ((n - 1) * π), 3.141592653589793) → i
  25. Rotate(A, (-i), J) → A'_1
  26. Rotate(B, (-i), J) → B'_2
  27. Rotate(C, (-i), J) → C'_1
  28. Polygon(A'_1, B'_2, C'_1) → poly1'_1, c'_1, a'_1, b'_2
  29. Rotate(g, (-i), J) → g'_1
  30. Rotate(h, (-i), J) → h'_1
  31. Rotate(k, (-i), J) → k'_1