Question

quadrilateral abcd is on a coordinate plane, where m∠a = m∠b. the quadrilateral is reflected across the x - axis to create quadrilateral abcd. which statement must be true about the angles in each quadrilateral? angle a is congruent to ∠b. angle b is congruent to ∠c. angle c is congruent to ∠d. angle d is congruent to ∠a.

Explanation:

Step1: Recall reflection property

A reflection is a rigid - motion. Rigid - motions preserve angle measures. That is, if a figure is reflected across a line, the angles in the original figure and the corresponding angles in the reflected figure are congruent. For quadrilateral \(ABCD\) reflected across the \(x\) - axis to get \(A'B'C'D'\), \(\angle A\cong\angle A'\), \(\angle B\cong\angle B'\), \(\angle C\cong\angle C'\), and \(\angle D\cong\angle D'\).

Answer:

No option is correct based on the given information as none of the options match the correct congruence relationships (\(\angle A\cong\angle A'\), \(\angle B\cong\angle B'\), \(\angle C\cong\angle C'\), \(\angle D\cong\angle D'\)) exactly. If we assume there is a mis - typing or oversight in the options, the general rule for reflection of a polygon across an axis is that each angle in the pre - image is congruent to its corresponding angle in the image.