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Sum of Angles in a Triangle by Mr. Coffie

Sum of Angles in a Triangle by Mr. Coffie
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2017-10-02 01:34
TriangleAngleGeometric Construction
This example demonstrates the property of the sum of angles in a triangle. Key mathematical concepts include the theorem of the sum of angles in a triangle. Using GeoGebra commands such as Point, Polygon, Line, Midpoint, Rotate, Angle, and Vector, it dynamically shows that the sum of the angles in a triangle is always 180 degrees. Suitable for middle school and above students to learn geometric construction and triangle properties.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Polygon(A, C, B) → poly1, b, a, c
  3. Line(C, c) → d
  4. Midpoint(C, A) → D
  5. Midpoint(C, B) → E
  6. Midpoint(A, B) → F
  7. Polygon(D, A, F) → poly2, f, d_1, a_1
  8. Polygon(F, E, B) → poly3, b_1, f_1, e
  9. Rotate(F, α, E) → F'_1
  10. Rotate(E, α, E) → E'
  11. Rotate(B, α, E) → B'
  12. Polygon(F'_1, E', B') → poly3', b', f'_1, e'
  13. Rotate(D, (-α), D) → D'
  14. Rotate(A, (-α), D) → A'
  15. Rotate(F, (-α), D) → F'
  16. Polygon(D', A', F') → poly2', f', d', a'
  17. Angle(B, A, C) → β
  18. Angle(F', A', D') → γ
  19. Angle(C, B, A) → δ
  20. Angle(E', B', F'_1) → ε
  21. Angle(A, C, B) → ζ
  22. Point(d) → G
  23. Point(d) → H
  24. Point(c) → I
  25. Point(c) → J
  26. Vector(G, H) → u
  27. Vector(I, J) → v