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Exterior Angle Sum Theorem

Exterior Angle Sum Theorem
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2012-03-14 12:33
TriangleAngleGeometric Construction
In collections Transformation-Rotation Transformation-Reflection Dilations Boy in Dilation
This example demonstrates the relationship between exterior and interior angles in a triangle. The Exterior Angle Sum Theorem states that an exterior angle equals the sum of the two non-adjacent interior angles. Key mathematical concepts include geometry, triangle angles, and construction techniques. Construction involves GeoGebra commands such as Polygon, Point, Angle, and Translate to create the triangle and mark the exterior angles. Suitable for middle or high school mathematics to understand geometric theorems and angle measurement.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Point(xAxis) → D
  3. Point(xAxis) → E
  4. Vector(D, E) → u
  5. Translate(A, u) → A'
  6. Translate(B, u) → B'
  7. Translate(C, u) → C'
  8. Polygon(A', B', C') → poly1', c', a', b'
  9. Angle(C, B, F) → α_1
  10. Angle(A, C, B) → β
  11. Angle(C, A, B) → γ
  12. Midpoint(a) → G
  13. Rotate(A, -α, G) → A'_1
  14. Rotate(B, -α, G) → B'_1
  15. Rotate(C, -α, G) → C'_1
  16. Polygon(A'_1, B'_1, C'_1) → poly1'_1, c'_1, a'_1, b'_1
  17. Angle(B'_1, A'_1, C'_1) → δ
  18. Angle(A'_1, C'_1, B'_1) → ε
  19. Angle(C', A', B') → ζ