Question

1. trapezoid klmn is reflected over the x-axis to form trapezoid wxyz. which statement is true?

the area of trapezoid klmn is greater than the area of trapezoid wxyz.
the angle measures of trapezoid klmn are less than the corresponding angle measures of trapezoid wxyz.
the sum of the angle measures of trapezoid klmn is twice the sum of the angle measures of trapezoid wxyz.
the side lengths of trapezoid klmn are congruent to the corresponding side lengths of trapezoid wxyz.

Explanation:

Step1: Recall Reflection Properties

Reflection over a line (here, x - axis) is a rigid transformation. Rigid transformations preserve side lengths and angle measures, and thus area.

Step2: Analyze Each Option

• Option 1: Reflection preserves area, so areas are equal. Eliminate.
• Option 2: Reflection preserves angle measures, so angles are equal. Eliminate.
• Option 3: Sum of angles in a trapezoid (quadrilateral) is \(360^\circ\) for both. So sum is same, not twice. Eliminate.
• Option 4: Rigid transformation (reflection) preserves side lengths, so corresponding sides are congruent. This is true.

Answer:

The side lengths of trapezoid KLMN are congruent to the corresponding side lengths of trapezoid WXYZ. (The option with this statement, likely the last one in the list of options)