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SAS Congruence Theorem & Triangle Congruence Transformation Demo

SAS Congruence Theorem & Triangle Congruence Transformation Demo
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2019-07-03 20:35
TriangleAngleTransformationGeometric Construction
This example demonstrates the proof of triangle congruence using the SAS theorem through geometric transformations. It involves core concepts like triangle congruence criteria, angle measurement, segment length, and geometric transformations (rotation, translation). Key GeoGebra commands and objects used in construction include Ray, Rotate, Angle, Point, Polygon, Segment, Circle, Intersect, CircleSector, Vector, and Translate. Suitable for high school geometry teaching to understand and apply the SAS congruence theorem.

GeoGebra Commands & Parameters

  1. Ray(A, B_1) → f
  2. Rotate(B_1, α, A) → B'
  3. Angle(B_1, A, B') → β
  4. Point(f) → B
  5. Ray(A, B') → g
  6. Point(g) → C
  7. Polygon(A, B, C) → poly1, h, i, j
  8. Segment(A, C) → k
  9. Segment(A, B) → l
  10. Circle(A, (0.2 * Min[k, l])) → c
  11. Intersect(c, f) → F,
  12. Intersect(c, k) → G,
  13. CircleSector(A, F, G) → d
  14. Point(xAxis) → H
  15. Vector((a, b)) → u
  16. Translate(A, u) → A'
  17. Translate(C, u) → D'
  18. Segment(A', D') → k'
  19. Translate(A, u) → A'_1
  20. Translate(B, u) → C'
  21. Translate(C, u) → D'_1
  22. Polygon(A'_1, C', D'_1) → poly1', d'_1, a'_1, c'
  23. Segment(D'_1, A'_1) → m
  24. Segment(C', A'_1) → n
  25. Segment(D'_1, C') → p
  26. Circle(A'_1, Radius[c]) → e
  27. Intersect(e, n, 1) → J
  28. Intersect(e, m, 1) → K
  29. CircleSector(A'_1, J, K) → q