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Angle Sum in a Triangle

Angle Sum in a Triangle
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2019-05-23 15:38
TriangleAngleGeometric Construction
In collections Learn GeoGebra Classic
This example demonstrates the angle sum property of triangles, showing that the sum of interior angles in any triangle is always 180 degrees. It involves core mathematical concepts like angle measurement, geometric proofs, and triangle properties. The construction uses commands such as Polygon for triangle creation, Angle for measuring angles, and Midpoint/Rotate for auxiliary constructions. Suitable for middle school students and above for learning geometric theorem verification and spatial reasoning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(poly1) → α, β, γ
  3. Midpoint(b) → D
  4. Midpoint(c) → E
  5. Rotate(A, δ, D) → A'
  6. Rotate(B, δ, D) → B'
  7. Rotate(C, δ, D) → C'
  8. Polygon(A', B', C') → poly1', c', a', b'
  9. Rotate(A, (-ε), E) → A'_1
  10. Rotate(B, (-ε), E) → B'_1
  11. Rotate(C, (-ε), E) → C'_1
  12. Polygon(A'_1, B'_1, C'_1) → poly1'_1, c'_1, a'_1, b'_1
  13. Angle(A', C', B') → ζ
  14. Angle(C'_1, B'_1, A'_1) → η