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SAS Triangle Congruence by FranklinCurtisMasonJunior

SAS Triangle Congruence by FranklinCurtisMasonJunior
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2015-06-13 23:23
TriangleVectorGeometric Construction
This example demonstrates the SAS Triangle Congruence Criterion. Using GeoGebra commands such as Vector, Rotate, and Translate, two triangles are constructed to show that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. This example is suitable for middle school geometry education, helping students understand the concept of triangle congruence.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(C, A, B) → α
  3. Line(D, E) → d
  4. Mirror(A, d) → R
  5. Mirror(B, d) → S
  6. Mirror(C, d) → T
  7. Polygon(R, S, T) → poly1', c', a', b'
  8. Angle(S, R, T) → β
  9. Vector(T, F) → u
  10. Translate(R, u) → R'
  11. Translate(S, u) → S'
  12. Translate(T, u) → T'
  13. Polygon(R', S', T') → poly1'', t', r', s'
  14. Rotate(R', (-γ), C) → R''
  15. Rotate(S', (-γ), C) → S''
  16. Rotate(T', (-γ), C) → T''
  17. Polygon(R'', S'', T'') → poly1''', t'', r'', s''
  18. Angle(S', R', T') → δ
  19. Angle(S'', R'', T'') → ε

AI Drawing Prompt Reference

Draw two triangles to demonstrate the SAS triangle congruence theorem. Start by drawing a triangle and labeling its two sides and included angle. Then construct another triangle using reflection and vector translation, ensuring its two sides and included angle match those of the first triangle. Finally, rotate the translated triangle to verify the congruence.
The prompt above was compiled from the original drawing commands and is for reference only.