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3 Pairs of Congruent Angles

3 Pairs of Congruent Angles
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2017-12-12 06:19
AngleSolid GeometryGeometric Construction
In collections Triangle Congruence Investigation Triangle Congruence Investigation
This example demonstrates the geometric relationships involving three pairs of congruent angles. It covers core math concepts such as congruent triangle criteria, angle relationships, and angle calculations in solid geometry. The construction utilizes GeoGebra commands/objects like Line, Rotate, Angle, Segment, Intersect, and Distance. Suitable for high school mathematics teaching to understand congruent triangle theorems and spatial geometric angle relationships.

GeoGebra Commands & Parameters

  1. Line(A_2, B) → f
  2. Rotate(A_2, 30°, B) → A
  3. Angle(A_2, B, A) → α
  4. Rotate(B, 100°, A) → B'
  5. Angle(B, A, B') → β
  6. Segment(A, B) → g
  7. Line(A, B') → h
  8. Intersect(f, h) → C
  9. Segment(A, C) → i
  10. Segment(C, B) → j
  11. Angle(A, C, B) → γ
  12. Line(A_1, E) → f_1
  13. Rotate(A_1, 30°, E) → D
  14. Angle(A_1, E, D) → α_1
  15. Rotate(E, 100°, D) → B'_1
  16. Angle(E, D, B'_1) → β_1
  17. Segment(D, E) → g_1
  18. Line(D, B'_1) → h_1
  19. Intersect(f_1, h_1) → F
  20. Segment(D, F) → i_1
  21. Segment(F, E) → j_1
  22. Angle(D, F, E) → γ_1
  23. Angle(E, D, F) → δ
  24. Angle(D, F, E) → ε
  25. Angle(F, E, D) → ζ
  26. Distance(B, C) → distanceBC
  27. Distance(A, B) → distanceAB
  28. Distance(C, A) → distanceCA
  29. Distance(D, E) → distanceDE
  30. Distance(D, F) → distanceDF
  31. Distance(F, E) → distanceFE