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Triangle Congruence Rules Demo

Triangle Congruence Rules Demo
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2018-11-12 19:40
TriangleAngleGeometric Construction
This example demonstrates the principles of triangle congruence rules (SSS, SAS, ASA, AAS) through geometric constructions. It involves core concepts like congruence, geometric transformations, and angle measurement. GeoGebra commands such as Point, Segment, Rotate, Angle, Ray, Circle, Intersect, and Polygon are used to build triangle models and illustrate the criteria. Suitable for middle school and above students for visualizing congruence theorems and applications.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 4]) → B
  2. Segment(A, B) → a
  3. Rotate(B, 70°, A) → B'
  4. Angle(B, A, B') → α
  5. Ray(A, B') → b
  6. Circle(A, 3) → c
  7. Intersect(c, b, 1) → C
  8. Polygon(A, B, C) → poligon1, c_1, a_1, b_1
  9. Point(Circle[D, 4]) → E
  10. Segment(D, E) → d
  11. Rotate(E, 60°, D) → E'
  12. Angle(E, D, E') → β
  13. Rotate(D, 310°, E) → D'
  14. Angle(D', E, D) → γ
  15. Ray(D, E') → e
  16. Ray(E, D') → f
  17. Intersect(e, f) → F
  18. Polygon(D, E, F) → poligon2, f_1, d_1, e_1
  19. Point(Circle[G, 4]) → H
  20. Segment(G, H) → g
  21. Circle(G, 3) → h
  22. Circle(H, 3.5) → k
  23. Intersect(h, k, 1) → I
  24. Polygon(G, H, I) → poligon3, i, g_1, h_1
  25. Point(Circle[J, 3.5]) → K
  26. Segment(J, K) → j
  27. Rotate(J, 280°, K) → J'
  28. Angle(J', K, J) → δ
  29. Ray(K, J') → l
  30. Circle(J, 4) → p
  31. Intersect(p, l, 1) → L
  32. Polygon(J, K, L) → poligon4, l_1, j_1, k_1

AI Drawing Prompt Reference

Draw a geometric figure consisting of three triangles. Each triangle is formed by three points defined through rotation, intersection, and rays. The first triangle uses points A and B, rotates to B', then intersects a ray and a circle to get point C. The second triangle starts from point D, rotates to E', then intersects rays and circles to get point F. The third triangle starts from point G, rotates to H', then intersects rays and circles to get point I. Ensure the figure clearly shows the construction process and key point relationships.
The prompt above was compiled from the original drawing commands and is for reference only.