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Congruent Triangles Naming & Congruence Reasoning

Congruent Triangles Naming & Congruence Reasoning
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2015-11-01 15:17
TriangleAngleTransformationGeometric Construction
This GeoGebra exercise dynamically demonstrates how to identify and name congruent triangles when triangles can be moved, rotated, or reflected. Core mathematical concepts include triangle congruence criteria (SSS, SAS, ASA) and the invariance of congruence under geometric transformations. Construction leverages GeoGebra commands such as Polygon, Vector, Angle, Intersect, Rotate, Segment, and Midpoint, involving vertices, side lengths, angle measurements, and polygon objects. Suitable for middle to high school geometry courses, it helps students develop spatial reasoning and understand the stability of congruence properties through dynamic construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Vector(P, A) → u
  3. Vector(P, B) → v
  4. Vector(P, C) → w
  5. Polygon(A_1, B_1, C_1) → poly1_1, c_1, a_1, b_1
  6. Vector(P_1, A_1) → u_1
  7. Vector(P_1, B_1) → v_1
  8. Vector(P_1, C_1) → w_1
  9. Angle(B, A, C) → α
  10. Angle(A, C, B) → β
  11. Angle(A_1, C_1, B_1) → γ
  12. Angle(B_1, A_1, C_1) → δ
  13. Intersect(Line[X_0, Rotate[Y_0, Ang_A, X_0]], Line[Y_0, Rotate[X_0, -(180° - Ang_C - Ang_A), Y_0]]) → Z_0
  14. Polygon(X_0, Y_0, Z_0) → poly2, z_0, x_0, y_0
  15. Rotate(Translate[Mirror[X_0, x = 0], (11, 0)], 155*°, (8, 0)) → X_1
  16. Textfield(text13) → Ans1
  17. Textfield(text14) → Ans2
  18. Segment(D, E) → r
  19. Midpoint(Segment[Intersect[Circle[A, r], b], Intersect[Circle[A, r], c]]) → F
  20. Midpoint(Segment[Intersect[Circle[C, r], a], Intersect[Circle[C, r], b]]) → G
  21. Midpoint(Segment[Intersect[Circle[A_1, r], b_1], Intersect[Circle[A_1, r], c_1]]) → H
  22. Midpoint(Segment[Intersect[Circle[C_1, r], a_1], Intersect[Circle[C_1, r], b_1]]) → I
  23. Rotate(Translate[Mirror[Y_0, x = 0], translate], 155*°, (8, 0)) → Y_1
  24. Rotate(Translate[Mirror[Z_0, x = 0], translate], 155*°, (8, 0)) → Z_1
  25. Angle(A_1, B_1, C_1) → ε
  26. Angle(C, B, A) → ζ
  27. Midpoint(Segment[Intersect[Circle[B, r], a], Intersect[Circle[B, r], c]]) → J
  28. Midpoint(Segment[Intersect[Circle[B_1, r], a_1], Intersect[Circle[B_1, r], c_1]]) → K