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Exterior Angle Theorem Demo

Exterior Angle Theorem Demo
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2022-03-19 00:16
TriangleAngleGeometric Construction
This example demonstrates the Exterior Angle Theorem, showing that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. It involves core concepts like exterior angles, interior angles, and triangle geometry. Construction uses commands such as Point, Polygon, Angle, Midpoint, Rotate, Segment, Ray, Line, Vector, and Translate to build the triangle and its exterior angles, with dynamic measurements to verify the theorem. Suitable for middle school and above students to visually understand geometric theorems and dynamic geometric transformations.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Point(f) → B
  3. Polygon(A, B, C) → t1, c, a, b
  4. Angle(C, B, A) → α
  5. Angle(B, A, C) → β
  6. Angle(A, C, B) → γ
  7. Midpoint(A, C) → D
  8. Midpoint(B, C) → E
  9. Polygon(E, B, (x(E), y(B))) → t2, g, e, b_1
  10. Rotate(t2, d, E) → t2'
  11. Polygon(A, D, (x(D), y(A))) → t3, h, a_1, d_1
  12. InteriorAngles(t2') → δ, ε, ζ
  13. Segment((x(B), y(B)), (x(E), y(E))) → i
  14. Rotate(i, d, E) → i'
  15. Segment((x(D), y(D)), (x(A), y(A))) → j
  16. Ray(A, C) → l
  17. Segment(A, C) → k
  18. Line(A, C) → n
  19. Point(n) → I
  20. Slope(n) → o
  21. Vector(A, J) → u
  22. Translate(t3, u) → t3'
  23. InteriorAngles(t3') → η, θ, ι
  24. Point(l) → K
  25. Angle(B, C, K) → κ

AI Drawing Prompt Reference

Draw a triangle ABC, connect points A and C to form line segment AC, and draw the exterior angles, including the extension of line segment BC through point B and the line segment AD through midpoint D of AC, and the line segment BE through midpoint E of BC. Use rotation and translation to demonstrate the exterior angle theorem, which states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
The prompt above was compiled from the original drawing commands and is for reference only.