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Maria determined that AABC is congruent with A A' B'C' because it was rotated 270° (counterclockwise). Do you agree with every...Question
Maria determined that 🔺ABC is congruent with 🔺 A' B'C' because it was rotated 270° (counterclockwise). Do you agree with every part of Maria's conclusion?
Statement #1: Yes. AABC was rotated 270° (counterclockwise) and is congruent with A A'B'C'.
Statement #2: No. AABC is congruent with AA' B'C", but it was rotated 90* (counterclockwise), not 270°.
Statement #3: No. AABC was rotated -90* (clockwise) and is not congruent with A'B'C".
(1 point)
Statement #
is correct.
Statement #1: Yes. AABC was rotated 270° (counterclockwise) and is congruent with A A'B'C'.
Statement #2: No. AABC is congruent with AA' B'C", but it was rotated 90* (counterclockwise), not 270°.
Statement #3: No. AABC was rotated -90* (clockwise) and is not congruent with A'B'C".
(1 point)
Statement #
is correct.
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Answered by
GPT-4o mini
To analyze Maria's conclusion, we need to understand the properties of rotation and congruence in geometry.
1. When a triangle is rotated 270° counterclockwise, this is equivalent to rotating it 90° clockwise. Therefore, if triangle ABC is indeed rotated 270° counterclockwise, then the resulting triangle A'B'C' will be congruent to triangle ABC (as rotations preserve congruence).
2. Someone states that if triangle ABC was rotated 90° (counterclockwise), then A'B'C' is indeed congruent to triangle ABC, and they mention 90° instead of 270°. Since 270° counterclockwise is equivalent to 90° clockwise, they are still correct in acknowledging that ABC and A'B'C' are congruent, but they have misidentified the type of rotation.
3. The final statement suggests that ABC was rotated -90° (clockwise), but this is also equivalent to the previous interpretations, as -90° clockwise is the same as 270° counterclockwise.
Considering all of this:
**Statement #1** is correct regarding the congruence, but misleading on the rotation description.
**Statement #2** incorrectly identifies the degree of rotation (it's 270° not 90°, but the congruence holds).
**Statement #3** declares a misinterpretation that leads to an incorrect conclusion about the congruence.
Thus, the conclusion can be drawn that **Statement #1 is the one that is correct, but not entirely accurate about the rotation degrees**.
Therefore, it would be best to say:
**Statement #1 is partially correct about the congruence but miscommunicates the rotation specificity. All others state the rotations in a manner that misrepresents congruence.**
In conclusion, the statement that supports the congruence (irrespective of how the rotation is termed) is the one affirmed as correct.
**Correct conclusion: Statement 1 is correct.**
1. When a triangle is rotated 270° counterclockwise, this is equivalent to rotating it 90° clockwise. Therefore, if triangle ABC is indeed rotated 270° counterclockwise, then the resulting triangle A'B'C' will be congruent to triangle ABC (as rotations preserve congruence).
2. Someone states that if triangle ABC was rotated 90° (counterclockwise), then A'B'C' is indeed congruent to triangle ABC, and they mention 90° instead of 270°. Since 270° counterclockwise is equivalent to 90° clockwise, they are still correct in acknowledging that ABC and A'B'C' are congruent, but they have misidentified the type of rotation.
3. The final statement suggests that ABC was rotated -90° (clockwise), but this is also equivalent to the previous interpretations, as -90° clockwise is the same as 270° counterclockwise.
Considering all of this:
**Statement #1** is correct regarding the congruence, but misleading on the rotation description.
**Statement #2** incorrectly identifies the degree of rotation (it's 270° not 90°, but the congruence holds).
**Statement #3** declares a misinterpretation that leads to an incorrect conclusion about the congruence.
Thus, the conclusion can be drawn that **Statement #1 is the one that is correct, but not entirely accurate about the rotation degrees**.
Therefore, it would be best to say:
**Statement #1 is partially correct about the congruence but miscommunicates the rotation specificity. All others state the rotations in a manner that misrepresents congruence.**
In conclusion, the statement that supports the congruence (irrespective of how the rotation is termed) is the one affirmed as correct.
**Correct conclusion: Statement 1 is correct.**
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