To determine which statement correctly explains the congruency of the trapezoids ABCD and A'B'C'D', we need to analyze the transformations described:
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Statement #1: States that the trapezoids are congruent because ABCD was reflected over the line y = x. This type of transformation preserves distance and shape, so it's a valid explanation for congruency.
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Statement #2: States that the trapezoids are congruent because ABCD was translated left 4 units and up 2 units. Translation also preserves congruency as it shifts a figure without changing its shape or size.
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Statement #3: States that the trapezoids are congruent because ABCD was rotated 270° (counterclockwise). Rotation maintains congruency since it involves turning the figure around a point without changing its size or shape.
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Statement #4: Similar to Statement #3, this one states that the trapezoids are congruent because ABCD was rotated 90° (counterclockwise). This is another valid transformation that preserves congruency.
Given that all four statements provide valid reasons for the congruency of trapezoids, but you can only select one, it would be essential to refer back to the image to confirm which transformation was actually applied.
If you see that the trapezoids appear to have maintained their shape and size and were moved to a new position without rotation or were reflected, then Statements #1 and #2 apply. If they were rotated, either Statement #3 or #4 would be correct depending on the direction and angle of rotation.
If you confirm a reflection took place, then: Statement #1 is correct. If a translation was the case: Statement #2 is correct. If they were rotated 270°: Statement #3 is correct. If they were rotated 90°: Statement #4 is correct.
Since I don't have access to the image, I can't determine which single statement is true. Please select and fill in the response accordingly based on your observations from the image.