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Exploring AAA Congruence by jroe

Exploring AAA Congruence by jroe
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2012-02-27 07:48
TriangleAngleGeometric Construction
In collections Similarity and Congruence Year 8 Pedagogies in Practice
This example demonstrates whether three equal angles can guarantee triangle congruence, involving core math concepts like triangle congruence criteria, geometric construction, and angle measurement. It uses commands like Rotate, Angle, Line, Point, Segment, Ray, Polygon in GeoGebra for exploration, suitable for high school students and teachers studying geometric proofs and triangle properties.

GeoGebra Commands & Parameters

  1. Rotate(B_1, Angle_A, A) → B'_1
  2. Angle(B_1, A, B'_1) → α
  3. Line(A, B'_1) → a
  4. Line(A, B_1) → b
  5. Point(b) → C
  6. Point(a) → B
  7. Segment(A, C) → c
  8. Segment(A, B) → d
  9. Rotate(A, Angle_B, B) → A'
  10. Angle(A, B, A') → β
  11. Ray(B, A') → e
  12. Point(e) → D
  13. Segment(B, D) → f
  14. Rotate(A, -Angle_C, C) → A'_1
  15. Angle(A'_1, C, A) → γ
  16. Ray(C, A'_1) → g
  17. Point(g) → E
  18. Segment(E, C) → h
  19. Polygon(A, C, B) → poly1, b_1, a_1, c_1
  20. Segment(D, E) → i
  21. Segment(A, B) → j
  22. Segment(B, C) → k
  23. Segment(A, C) → l