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Triangle Angle-Sum Theorem

Triangle Angle-Sum Theorem
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2013-08-15 06:10
TriangleAngleGeometric Construction
In collections Intro to Angles
This example demonstrates the triangle angle-sum theorem. By constructing a triangle and its angles, it shows that the sum of the three interior angles of a triangle is always 180 degrees. GeoGebra commands used include Segment, Midpoint, Circle, Intersect, CircleSector, Rotate, Sector, and Line. Suitable for middle school and above students to learn geometric construction and triangle properties.

GeoGebra Commands & Parameters

  1. Segment(B, C) → a
  2. Segment(C, A) → b
  3. Segment(A, B) → c
  4. Midpoint(c) → D
  5. Circle(B, E) → d
  6. Circle(C, F) → e
  7. Intersect(d, c, 1) → G
  8. Intersect(e, b, 1) → H
  9. CircleSector(B, E, G) → f
  10. CircleSector(C, H, F) → g
  11. Rotate(B, (-γ), D) → B'
  12. Rotate(E, (-γ), D) → E'
  13. Rotate(G, (-γ), D) → G'
  14. Sector(Rotate[Circle[B, E], (-γ), D], E', G') → A_1
  15. Midpoint(b) → I
  16. Rotate(C, γ, I) → C'
  17. Rotate(H, γ, I) → H'
  18. Rotate(F, γ, I) → F'
  19. Sector(Rotate[Circle[C, H], γ, I], H', F') → A_2
  20. Circle(A, 0.5) → h
  21. Intersect(h, c) → J,
  22. Intersect(h, b) → K,
  23. CircleSector(A, J, K) → k
  24. Line(A, a) → l

AI Drawing Prompt Reference

Draw a triangle ABC with sides a, b, and c connecting vertices A, B, and C. Construct circles d and e with midpoint D of side c, and find their intersections with sides at points G and H. Rotate points B, E, G and C, H, F to form sectors A_1 and A_2. Rotate points C, H, F around midpoint I of side b to form another sector A_2. Finally, draw a circle h with center A and radius 0.5, intersecting sides b and c at points J and K to form sector k.
The prompt above was compiled from the original drawing commands and is for reference only.