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ASA Congruence

ASA Congruence
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2017-04-27 11:35
TriangleAngleGeometric Construction
This example demonstrates the ASA (Angle-Side-Angle) congruence of triangles. It involves the core mathematical concept of triangle congruence conditions. Using GeoGebra commands such as Point, Segment, Rotate, Angle, Intersect, and Polygon, one can construct triangles that meet the ASA conditions. Suitable for middle school and above students to learn about triangle congruence conditions and geometric construction.

GeoGebra Commands & Parameters

  1. Point(Circle[A, b]) → B
  2. Segment(A, B) → f
  3. Rotate(A, (-β), B) → A'
  4. Angle(A', B, A) → γ
  5. Rotate(B, α, A) → B'
  6. Angle(B, A, B') → δ
  7. Segment(A, B') → g
  8. Segment(B, A') → h
  9. Intersect(g, h) → C
  10. Polygon(C, A, B) → poly1, b_1, c, a
  11. Point(Circle[F, b]) → E
  12. Segment(F, E) → f_1
  13. Rotate(F, (-β), E) → A'_1
  14. Angle(A'_1, E, F) → γ_1
  15. Rotate(E, α, F) → B'_1
  16. Angle(E, F, B'_1) → δ_1
  17. Segment(F, B'_1) → g_1
  18. Segment(E, A'_1) → h_1
  19. Intersect(g_1, h_1) → G
  20. Polygon(G, F, E) → poly1_1, b_2, c_1, a_1
  21. Angle(E, F, G) → ε
  22. Angle(G, E, F) → ζ
  23. Segment(A, C) → i
  24. Segment(C, B) → j