Question
Which explanation for the congruency of the trapezoids is correct?
Statement #1: The trapezoids are congruent because ABCD was reflected over the y = x.
Statement #2: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units.
Statement #3: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise).
Statement #4: The trapezoids are congruent because ABCD was rotated 90°(counterclockwise).
Statement #1: The trapezoids are congruent because ABCD was reflected over the y = x.
Statement #2: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units.
Statement #3: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise).
Statement #4: The trapezoids are congruent because ABCD was rotated 90°(counterclockwise).
Answers
GPT-4o mini
To determine which statement explains the congruency of the trapezoids, we need to consider how transformations affect the congruence of geometric figures:
1. **Reflection**: Reflecting a figure over a line (like \(y = x\)) preserves congruence. Thus, statement #1 could be correct if the trapezoids are indeed the result of such a reflection.
2. **Translation**: Translating a figure (shifting it left or right, up or down) also preserves congruence. Therefore, statement #2 could be correct if the trapezoids resulted from the described translation.
3. **Rotation**: Rotating a figure by any angle also preserves congruence. This means that either statement #3 (rotating 270° counterclockwise) or statement #4 (rotating 90° counterclockwise) could be correct if the trapezoids are the result of such rotations.
In summary, all four statements involve transformations (reflection, translation, rotation) that preserve congruence. So, technically, if any of these transformations accurately describe how trapezoid ABCD relates to the other trapezoid, that statement would be correct.
To determine which specific explanation applies, we would need more information about the relationship between trapezoid ABCD and the other trapezoid in question (such as their coordinates or shapes). Without this additional context, we can't definitively say which statement is the sole correct explanation.
1. **Reflection**: Reflecting a figure over a line (like \(y = x\)) preserves congruence. Thus, statement #1 could be correct if the trapezoids are indeed the result of such a reflection.
2. **Translation**: Translating a figure (shifting it left or right, up or down) also preserves congruence. Therefore, statement #2 could be correct if the trapezoids resulted from the described translation.
3. **Rotation**: Rotating a figure by any angle also preserves congruence. This means that either statement #3 (rotating 270° counterclockwise) or statement #4 (rotating 90° counterclockwise) could be correct if the trapezoids are the result of such rotations.
In summary, all four statements involve transformations (reflection, translation, rotation) that preserve congruence. So, technically, if any of these transformations accurately describe how trapezoid ABCD relates to the other trapezoid, that statement would be correct.
To determine which specific explanation applies, we would need more information about the relationship between trapezoid ABCD and the other trapezoid in question (such as their coordinates or shapes). Without this additional context, we can't definitively say which statement is the sole correct explanation.