To determine the correct explanation for the congruency of the trapezoids, we need to analyze the effects of the transformations described.
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Rotation of 90° (counterclockwise): This transformation would change the orientation of the figure but generally would not preserve the shape or size in terms of congruency with another shape unless the original and resulting figures have specific corresponding dimensions.
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Reflection over the line y = x: This transformation flips the figure over the line y = x. If trapezoid ABCD is reflected properly, the resulting figure will maintain congruency with the original trapezoid, provided the corresponding dimensions are equal.
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Rotation of 270° (counterclockwise): Rotating the figure 270° (or 90° clockwise) would also change the orientation without affecting the size or shape, meaning the figure would remain congruent to its original shape.
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Translation left 4 units and up 2 units: Translation moves the entire figure without altering its shape or dimensions, meaning the two trapezoids would be congruent.
Given this analysis, all the transformations (rotation of 90°, rotation of 270°, reflection over y = x, and the translation) could result in congruency between the trapezoids depending on the specific details of the trapezoids' positions and dimensions. However, translations and reflections are the most straightforward congruency-preserving transformations.
If you can provide more context about the trapezoids or a diagram, I can help identify the correct transformation more accurately. If I had to select one general answer based on common scenarios where figures are congruent, I would say:
- The trapezoids are congruent because ABCD was reflected over the line y = x (as reflection is often a clear congruence transformation when testing for congruency).
If there is a specific case or image in question, please provide that for a more precise answer!
2 answers