To determine which explanation for the congruency of the trapezoids is correct, we need to analyze the transformations mentioned:
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Reflection over the line y = x: This transformation flips the trapezoid over the line y = x, which can lead to a congruent figure depending on the original position and orientation of trapezoid ABCD.
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Translation left 4 units and up 2 units: Translation moves all points of the figure in the same direction and by the same distance, so the shape and size remain unchanged, making the figures congruent.
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Rotation 90° (counterclockwise): Rotating a figure 90° counterclockwise can create a congruent figure, but the resulting orientation may not match exactly depending on the original trapezoid.
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Rotation 270° (counterclockwise): Similar to a 90° rotation, this transformation can also create a congruent figure, although the orientation will differ from the original.
Since both reflection and translation maintain congruence, we can quickly assess which explanations are valid. However, the question usually asks for the most appropriate or common transformation that leads to congruency:
- Translation is the simplest and most straightforward transformation to explain congruence without changing the orientation.
Thus, the correct explanation for the congruency of the trapezoids is:
The trapezoids are congruent because ABCD was translated left 4 units and up 2 units.
1 answer