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Congruent Triangles Exercise by Kawa Chan

Congruent Triangles Exercise by Kawa Chan
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2015-11-01 15:19
TriangleAngleGeometric Construction
This example demonstrates how to name congruent triangles with reasons. The triangles are movable, rotatable, and reflectable. Key math concepts include congruence, geometric transformations, and angle measurement. Construction highlights the use of GeoGebra commands such as Polygon, Vector, Angle, Intersect, Textfield, Segment, Midpoint, Rotate, and Vertex. Suitable for middle school and above, focusing on geometric constructions and congruence criteria in mathematics education.

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[Y_0, Side_a], x = x(X_0)) → 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(Polygon[Mirror[X_0, x = 0], Mirror[Y_0, x = 0], Mirror[Z_0, x = 0]], 2.1790419057051063, (5.011056281987284, 4.704101305477666)) → poly3
  27. Vertex(poly3, 1) → X_1
  28. Vertex(poly3, 2) → Y_1
  29. Vertex(poly3, 3) → Z_1