When trapezoid KLMN is reflected over the x-axis to form trapezoid WXYZ, the properties of reflection tell us that the shapes maintain their size and shape, but their orientation and position may change.
In this case, the reflection over the x-axis results in each point of trapezoid KLMN having its y-coordinate negated. For example, if point K has coordinates (x, y), after reflection it will become point W with coordinates (x, -y). The same applies to the other points of the trapezoid.
As a result:
- The corresponding sides of trapezoids KLMN and WXYZ will have the same lengths because reflection preserves the distances between points.
- Therefore, the lengths of the sides in trapezoid KLMN will be congruent to the lengths of the sides in trapezoid WXYZ.
So yes, the side lengths are congruent after the reflection.