To evaluate Maria's conclusion about the triangles \( \triangle ABC \) and \( \triangle A'A'B'C' \), let's break down the information provided:
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Statement #1 claims that \( \triangle ABC \) is congruent to \( \triangle A'A'B'C' \) because it was rotated \( 270^\circ \) (counterclockwise). This is correct; a \( 270^\circ \) counterclockwise rotation is equivalent to a \( 90^\circ \) clockwise rotation, which would produce a congruent triangle. However, there's ambiguity because the triangle's designation (the labels) isn't clear if the triangles mentioned are indeed the same points.
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Statement #2 disagrees, stating that \( \triangle ABC \) is congruent with \( \triangle A'A'B'C' \), but was rotated \( 90^\circ \) (counterclockwise) instead of \( 270^\circ \). This could potentially also be true if the congruency is valid from the correct rotation. The designation of points hasn’t been verified.
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Statement #3 also disagrees, pointing out that \( \triangle ABC \) was rotated \( -90^\circ \) (clockwise) and is not congruent with \( A'B'C' \). This would be incorrect in the context of congruency, as a rotation (whether clockwise or counterclockwise) maintains the triangle's congruency if triangles are labeled appropriately.
Based on the consideration of these statements, it appears:
- Statements 1 and 2 could potentially both be correct depending on the specifics of the orientation and labeling of the triangles.
- Statement 3 is incorrect in terms of the conclusion about congruence but may argue based on the rotation direction.
If the triangles \( AA'B'C' \) and \( AABC \) correspond correctly, based on the congruence: It appears Statement #2 could accurately reflect the scenario if verified that the triangles are properly congruent with respect to how they are rotated.
Thus, Statement #2 seems to be the correct answer based on the details provided. Your choice is Statement #2.
1 answer