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Trapezoid `KLMN`is reflected over the x-axis to form trapezoid `WXYZ`. Which statement is true?

The area of trapezoid "K" "L" "M" "N"
KLMN is greater than the area of trapezoid "W" "X" "Y" "Z"
WXYZ.

The angle measures of trapezoid "K" "L" "M" "N"
KLMN are less than the corresponding angle measures of trapezoid "W" "X" "Y" "Z"
WXYZ.

The sum of the angle measures of trapezoid "K" "L" "M" "N"
KLMN is twice the sum of the angle measures of trapezoid "W" "X" "Y" "Z"
WXYZ.

The side lengths of trapezoid "K" "L" "M" "N"
KLMN are congruent to the corresponding side lengths of trapezoid "W" "X" "Y" "Z"
WXYZ.

1 answer

When trapezoid \( KLMN \) is reflected over the x-axis to form trapezoid \( WXYZ \), the following considerations apply:

  1. Area: The area of trapezoid \( KLMN \) is equal to the area of trapezoid \( WXYZ \) because reflection does not change the dimensions or size of the figure. Therefore, the statement that the area of trapezoid \( KLMN \) is greater than the area of trapezoid \( WXYZ \) is false.

  2. Angle Measures: The angles of trapezoid \( KLMN \) are congruent to the angles of trapezoid \( WXYZ \) because reflection does not change the angle measures. Therefore, the statement that the angle measures of trapezoid \( KLMN \) are less than those of trapezoid \( WXYZ \) is false.

  3. Sum of Angle Measures: The sum of the angle measures of both trapezoids is equal. The sum of the interior angles of any trapezoid is always the same, regardless of its position or orientation. Therefore, the statement that the sum of the angle measures of trapezoid \( KLMN \) is twice the sum of those of trapezoid \( WXYZ \) is false.

  4. Side Lengths: Since trapezoid \( KLMN \) is only reflected and not resized, the side lengths of trapezoid \( KLMN \) are congruent to the corresponding side lengths of trapezoid \( WXYZ \). Therefore, this statement is true.

In summary, the correct statement is:

The side lengths of trapezoid \( KLMN \) are congruent to the corresponding side lengths of trapezoid \( WXYZ \).