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AAS Congruence Proof Step 3

AAS Congruence Proof Step 3
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2016-01-22 07:29
TriangleTransformationGeometric Construction
This example demonstrates the third step of the AAS congruence proof. The key mathematical concept involved is triangle congruence. Using GeoGebra commands such as Polygon, Angle, Ray, Rotate, Circle, and Intersect, the construction of triangle rotation and congruence proof is illustrated. Suitable for middle and high school students learning triangle congruence proof.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(C, A, B) → α
  3. Angle(A, B, C) → β
  4. Ray(A', D) → d
  5. Rotate(A', α, A') → A''
  6. Rotate(D, α, A') → D'
  7. Ray(A'', D') → d'
  8. Circle(A', c) → e
  9. Intersect(e, d', 1) → B'
  10. Rotate(A', β, B') → A''_1
  11. Ray(B', A''_1) → f
  12. Intersect(d, f) → C'
  13. Polygon(A', B', C') → poly2, c', a', b'
  14. Angle(C', A', B') → α'
  15. Angle(A', B', C') → β'
  16. Angle(B', C', A') → γ'
  17. Angle(B, C, A) → γ

AI Drawing Prompt Reference

Draw a triangle with labeled angles and included side, then rotate the triangle around one vertex, rotate a ray using the new vertex and another vertex, find the intersection of a circle centered at the original vertex with the rotated ray, and rotate again using the new intersection point to complete the construction of two similar triangles.
The prompt above was compiled from the original drawing commands and is for reference only.