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AAS Triangle Congruence Demonstration

AAS Triangle Congruence Demonstration
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2015-10-14 03:49
TriangleAngleGeometric Construction
In collections Triangle Congruence
This example demonstrates the AAS (Angle-Angle-Side) condition for triangle congruence. It involves core mathematical concepts such as triangle congruence criteria, angle and side measurements, and dynamic geometric transformations. The construction utilizes GeoGebra commands and objects like Ray, Circle, Intersect, Point, DynamicCoordinates, Rotate, Angle, Segment, and If. It is suitable for high school mathematics education to visually illustrate and verify the application of the AAS congruence condition.

GeoGebra Commands & Parameters

  1. Ray(A, A_2) → a
  2. Circle(A, Side3) → c
  3. Intersect(c, a, 1) → B_2
  4. Point(a) → InvB
  5. DynamicCoordinates(InvB, If[Distance[B_2, InvB] < Sticky, x(B_2), x(InvB)], If[Distance[B_2, InvB] < Sticky, y(B_2), y(InvB)]) → B
  6. Rotate(A, Angle1, A) → C_1
  7. Rotate(A_2, Angle1, A) → A'
  8. Ray(C_1, A') → a'
  9. Circle(A, Side2) → d
  10. Intersect(d, a', 1) → C_2
  11. Point(a') → InvC
  12. DynamicCoordinates(InvC, If[Distance[C_2, InvC] < Sticky, x(C_2), x(InvC)], If[Distance[C_2, InvC] < Sticky, y(C_2), y(InvC)]) → C
  13. Circle(B, NonIncSide) → e
  14. Angle(B, A, C) → α
  15. Segment(A, B) → f
  16. Segment(A, C) → g
  17. Point(f) → D
  18. Rotate(D, (-Angle2), B) → D'
  19. Ray(B, D') → b
  20. Circle(B, NonIncSide) → h
  21. Intersect(h, b, 1) → C_1''
  22. Segment(B, C_1'') → i
  23. Angle(C_1'', B, A) → β
  24. If(Distance[C, C_1''] < 0.2, Polygon[A, B_2, C_2]) → poly1