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Angle Sum of a Triangle

Angle Sum of a Triangle
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2015-11-10 09:29
TriangleAngleGeometric Construction
This example demonstrates the geometric phenomenon that the sum of interior angles in any triangle is always 180°. Core math concepts include angle measurement, triangle geometry, and geometric proofs. Construction highlights involve commands/objects like Polygon, Midpoint, If, Translate, and Angle from GeoGebra. Suitable for middle school and above students learning basic triangle properties or as a mathematical visualization teaching tool.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(c) → D
  3. Midpoint(a) → E
  4. Midpoint(b) → F
  5. If(t < 1, t, 1) → t1
  6. If(t > 1, t - 1, 0) → t2
  7. Polygon(D, E, C, F) → poly2, d, e, c_1, f
  8. Translate(Polygon[Rotate[A, (180° * t1), D], Rotate[D, (180° * t1), D], Rotate[F, (180° * t1), D]], Vector[(t2 * Vector[B, C])]) → poly3
  9. Translate(B, Vector[(t2 * Vector[B, C])]) → B'
  10. Translate(E, Vector[(t2 * Vector[B, C])]) → E'
  11. Translate(D, Vector[(t2 * Vector[B, C])]) → D'
  12. Polygon(B', E', D') → poly4, d', b', e'
  13. Angle(A, C, B) → γ
  14. Angle(Translate[E, Vector[(t2 * Vector[B, C])]], Translate[B, Vector[(t2 * Vector[B, C])]], Translate[D, Vector[(t2 * Vector[B, C])]]) → β
  15. Angle(Translate[Rotate[D, (180° * t1), D], Vector[(t2 * Vector[B, C])]], Translate[Rotate[A, (180° * t1), D], Vector[(t2 * Vector[B, C])]], Translate[Rotate[F, (180° * t1), D], Vector[(t2 * Vector[B, C])]]) → α