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Trapezoid KLMN is reflected over the x-axis to form trapezoid WXYZ.

Which statement is true?

1 The area of trapezoid KLMN is greater than the area of trapezoid WXYZ
2 The angle measures of trapezoid KLMN are less than the corresponding angle measures of trapezoid WXYZ.
3 The sum of the angle measures of trapezoid KLMN is twice the sum of the angle measures of trapezoid WXYZ.
4 The side lengths of trapezoid KLMN are congruent to the corresponding side lengths of trapezoid WXYZ.

1 answer

When trapezoid KLMN is reflected over the x-axis to form trapezoid WXYZ, the following statements can be evaluated:

  1. The area of trapezoid KLMN is greater than the area of trapezoid WXYZ.
    This statement is false. The area of a figure does not change under reflection.

  2. The angle measures of trapezoid KLMN are less than the corresponding angle measures of trapezoid WXYZ.
    This statement is false. Reflection does not change angle measures; they remain the same.

  3. The sum of the angle measures of trapezoid KLMN is twice the sum of the angle measures of trapezoid WXYZ.
    This statement is also false. Since the angles remain unchanged, the sums of the angle measures will be equal.

  4. The side lengths of trapezoid KLMN are congruent to the corresponding side lengths of trapezoid WXYZ.
    This statement is true. Reflection preserves distances and hence, the corresponding side lengths remain congruent.

Based on the evaluations, the correct statement is:

4. The side lengths of trapezoid KLMN are congruent to the corresponding side lengths of trapezoid WXYZ.