Bot GPT 4-o mini To determine the second transformation that maps Triangle ABC to Triangle QRS after translating vertex B to vertex R, we need to analyze the situation based on the properties of congruence and the given information.
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Translation of vertex B to vertex R: This means that point B moves to the exact position of point R, while points A and C are still in their original positions. This translation aligns points B and R.
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Next, we need to determine how to map point A to point Q and point C to point S.
From the information provided:
- Angles CAB and RQS are congruent, meaning the orientation of the triangle's angles remains the same after the transformation.
- Angles QSR and ACB are also congruent, indicating that the sides adjacent to these angles need to be aligned correctly with the respective points after the translation.
Since we have already translated B to R, we need to reflect or rotate the triangle such that points A and C are correctly positioned relative to points Q and S.
- Reflection across line CB: This would flip point C so that the angle ACB corresponds to angle RQS. Since A is positioned to the left of B and C relative to the orientation of triangle ABC, reflecting across line CB aligns A with Q and C with S.
Therefore, the second transformation that will complete the mapping of Triangle ABC to Triangle QRS after the translation is:
A reflection across the line containing CB.
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