Bot GPT 4-o mini In the scenario described, we have two triangles \( ABC \) and \( A'B'C' \) which are congruent by the HL theorem (Hypotenuse-Leg theorem). Given that angles \( A'C'B \) and \( ACB \) are right angles, and that the lengths \( C'A' \) and \( CA \) are congruent, as well as \( A'B \) being congruent to \( AB \), it indicates that the triangles are positioned such that all corresponding sides and angles are congruent.
Since we are looking for a single rigid transformation that maps triangle \( ABC \) onto triangle \( A'B'C' \), and we have congruency and matching right angles, the most likely rigid transformation is a reflection.
This is because the triangles share vertex \( B \), and the right angles allow for the possibility of reflection across the line that bisects the angle at \( B \) (the line segment \( BC \) can act as the axis of reflection).
Thus, the transformation that maps triangle \( ABC \) to triangle \( A'B'C' \) is a reflection.
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