Which explanation for the congruency of the trapezoids is correct? Statement #1: The trapezoids are congruent because ABCD was reflected over the line 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). (1 point) Statement # is correct.

Answer 1

To determine which statement correctly explains the congruency of the trapezoids, we need to analyze what transformations maintain congruency.

• Reflections (like the reflection over y=x) preserve distances and angles, thus they maintain congruency.
• Translations also preserve distance and angles, so this also results in congruent figures.
• Rotations (both 90° and 270°) also preserve congruency since they maintain distances and angles.

Since all transformation types mentioned preserve congruency, we cannot definitively say one specific statement is correct without additional context about the trapezoids. However, if all transformations are applied correctly, any one of the statements can be considered correct under the right circumstances.

If you're looking for a singular answer based on standard practices in geometry, all of these statements indicate valid methods to achieve congruency. If you have the specific context or relationships between the trapezoids in question, I would need that information to provide a more targeted answer. As it stands:

All statements (Statement #1, Statement #2, Statement #3, and Statement #4) could potentially be correct regarding congruency, depending on the specific transformations performed on trapezoid ABCD.