Question

Which explanation for the congruency of the trapezoids is correct? Statement #1: The trapezoids are congruent because ABCD was reflected over the 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) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Statement #Response area is correct.

Answer 1

To determine which statement is correct regarding the congruency of the trapezoids, we need to evaluate each statement based on the transformations described.

1. **Statement #1: The trapezoids are congruent because ABCD was reflected over the y = x.**
- A reflection over the line y = x would create a congruent trapezoid. This statement could be correct.

2. **Statement #2: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units.**
- A translation does preserve congruence, so this statement is also correct.

3. **Statement #3: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise).**
- A rotation also preserves congruence, making this statement correct as well.

4. **Statement #4: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise).**
- Similar to Statement #3, a rotation preserves congruence, so this statement is also correct.

Given the analysis above, **all statements imply congruence. However, if only one statement can be chosen as the primary explanation, it typically depends on context or specific geometric information provided.** If you need to select one, any of these statements could be appropriate depending on the details of the trapezoids. Without additional context, it's impossible to definitively declare one option as the only explanation.

If faced with the task of selecting just one statement, I recommend **Statement #2: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units**, as translation is one of the simplest transformations to illustrate congruence without altering shape or orientation.

However, if all statements are to reflect the correct reasoning for congruent trapezoids based on transformations, than all listed statements can be justified as correct.