To determine which statement correctly explains the congruency of the trapezoids, let's analyze each statement carefully:
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Statement #1: The trapezoids are congruent because ABCD was reflected over the y = x.
- A reflection over the line \(y = x\) will create a congruent shape (trapezoid) since it preserves distances and angles.
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Statement #2: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units.
- A translation also preserves distances and angles, meaning the trapezoids formed by translating the original trapezoid will be congruent.
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Statement #3: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise).
- A rotation, regardless of the angle, preserves distance and angle measures, leading to congruent trapezoids.
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Statement #4: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise).
- Like statement #3, a rotation of any degree (including 90°) results in congruent figures.
Since all statements provided explain congruency correctly due to either reflection, translation, or rotation, any of the statements can be considered correct. However, to determine the most fitting explanation without additional context (such as a specific diagram), you might select any of those that apply based on validity.
If there is a requirement for just one statement, you might select the first one or any of the others, acknowledging they all are correct.
If you are limited to selecting just one response, I would suggest:
Response Area: Statement #1 is correct.
However, you can also choose any of the statements as being equally valid explanations for the congruency of the trapezoids.
1 answer