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Congruent Triangles Exercise 2

Congruent Triangles Exercise 2
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2015-11-01 15:18
TriangleAngleTransformationGeometric Construction
This example demonstrates how to name congruent triangles and provide reasons. Users can move, rotate, and reflect the triangles. Using GeoGebra commands such as Polygon, Vector, Angle, Intersect, Textfield, Segment, Midpoint, and Rotate, one can construct and verify congruent triangles. Suitable for middle school and above students to learn about geometric transformations and congruent triangles.

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(Circle[X_0, Side_b], Circle[Y_0, Side_a]) → Z_0, L, ,
  14. Polygon(X_0, Y_0, Z_0) → poly2, z_0, x_0, y_0
  15. Textfield(text13) → Ans1
  16. Textfield(text14) → Ans2
  17. Segment(D, E) → r
  18. Midpoint(Segment[Intersect[Circle[A, r], b], Intersect[Circle[A, r], c]]) → F
  19. Midpoint(Segment[Intersect[Circle[C, r], a], Intersect[Circle[C, r], b]]) → G
  20. Midpoint(Segment[Intersect[Circle[A_1, r], b_1], Intersect[Circle[A_1, r], c_1]]) → H
  21. Midpoint(Segment[Intersect[Circle[C_1, r], a_1], Intersect[Circle[C_1, r], b_1]]) → I
  22. Angle(A_1, B_1, C_1) → ε
  23. Angle(C, B, A) → ζ
  24. Midpoint(Segment[Intersect[Circle[B, r], a], Intersect[Circle[B, r], c]]) → J
  25. Midpoint(Segment[Intersect[Circle[B_1, r], a_1], Intersect[Circle[B_1, r], c_1]]) → K
  26. Rotate(Translate[Mirror[X_0, x = 0], translate], -(180° - Angle[Y_0, X_0, Z_0]), (11, 0)) → X_1
  27. Rotate(Translate[Mirror[Y_0, x = 0], translate], -(180° - Angle[Y_0, X_0, Z_0]), (11, 0)) → Y_1
  28. Rotate(Translate[Mirror[Z_0, x = 0], translate], -(180° - Angle[Y_0, X_0, Z_0]), (11, 0)) → Z_1

AI Drawing Prompt Reference

Draw two congruent triangles ABC and A₁B₁C₁. Use point P to translate and rotate triangle ABC to form A₁B₁C₁. Construct corresponding sides and angles, and use midpoints and rotations to ensure the triangles are congruent. Start by drawing triangle ABC, then translate and rotate it using point P.
The prompt above was compiled from the original drawing commands and is for reference only.