ASA Congruence: Constructing Congruent Triangles via Rotation and Intersection

ASA Congruence: Constructing Congruent Triangles via Rotation and Intersection
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2017-04-27 11:46
① This example demonstrates how to construct two congruent triangles using the ASA (Angle-Side-Angle) criterion, visually confirming the congruence theorem. ② Core mathematical concepts include triangle congruence (ASA), angle measurement, segment length, rotation, and intersection of lines. ③ Construction steps: Using GeoGebra commands Point, Segment, Rotate, Angle, Line, and Intersect, points A, B, C and rotated points A', B' are created; angles α, β, γ and segments define the sides; lines and intersections determine vertices D, E, F, yielding two congruent triangles. ④ Suitable for middle school geometry lessons to illustrate congruence conditions, and as a dynamic tool for exploring corresponding parts under rotation.

GeoGebra Commands & Parameters

  1. Point(Circle[A, b]) → B
  2. Segment(A, B) → f
  3. Rotate(B, α, A) → B'
  4. Angle(B, A, B') → γ
  5. Line(A, B') → g
  6. Rotate(A, (-β), B) → A'
  7. Angle(A', B, A) → δ
  8. Line(B, A') → h
  9. Intersect(h, g) → C
  10. Segment(A, C) → i
  11. Segment(C, B) → j
  12. Point(Circle[D, b]) → E
  13. Segment(D, E) → k
  14. Rotate(E, α, D) → E'
  15. Angle(E, D, E') → ε
  16. Line(D, E') → l
  17. Rotate(D, (-β), E) → D'
  18. Angle(D', E, D) → ζ
  19. Line(E, D') → m
  20. Intersect(m, l) → F
  21. Segment(D, F) → n
  22. Segment(F, E) → p
  23. Angle(A, C, B) → η
  24. Angle(D, F, E) → θ
  25. Segment(A, B) → q