Which explanation for the congruency of the trapezoids is correct?

Question

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)
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 areais true.
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Answer 1

To determine which statements about the congruency of the trapezoids are correct, we need to analyze the transformations described in each statement:

1. Statement #1: The trapezoids are congruent because ABCD was reflected over the line y = x.

   • This statement is true. A reflection preserves congruency.

2. Statement #2: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units.

   • This statement is true. A translation preserves congruency.

3. Statement #3: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise).

   • This statement is true. A rotation preserves congruency.

4. Statement #4: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise).

   • This statement is also true. A rotation preserves congruency.

Since all the statements provide valid reasons for the trapezoids being congruent, the correct response would include all of them. However, if you are only to choose one statement based on typical assessment practices where you might get a specific question regarding a certain transformation, you can select any that you believe is most relevant or pertinent to the given geometric situation.

To proceed with inputting your responses based on this analysis:

1. If prompted with a selection, choose:
   • Statement #1
   • Statement #2
   • Statement #3
   • Statement #4

If you need to pick just one as the most relevant answer (often might depend on the context given), then choose Statement #1, Statement #2, Statement #3, or Statement #4, as they are all valid.