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Sum of Angles in a Triangle by GreenMaths

Sum of Angles in a Triangle by GreenMaths
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2013-03-19 04:38
TriangleAngleVectorGeometric ConstructionSlider Animation
In collections Introduction to Geometry
This example demonstrates the proof that the sum of angles in a triangle is 180 degrees through an animation. It extends one side of the triangle to construct auxiliary lines, then uses angle properties and transformations to show the invariance of the angle sum. GeoGebra commands used include point, polygon, line, midpoint, rotate, angle, and vector. Suitable for middle school and above students to learn geometric transformations and proof methods.

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

AI Drawing Prompt Reference

Draw a triangle ABC, extend side BC to point D and construct line CD. Find the midpoints of AB and BC, name them E and F. Rotate point F and B around point E to get F' and B', then rotate point A and F around point D to get A' and F'. Construct triangle A'B'C' and measure the angles BAC, ABC, and ACB, their sum should be close to 180 degrees.
The prompt above was compiled from the original drawing commands and is for reference only.