Maritza draws a rectangle on the coordinate plane and labels the vertices A , B , C , and D . She then reflects the figure across the x -axis to get rectangle A′B′C′D′ . What is the measure of angle D′ in the reflected rectangle?
When a figure is reflected across the x-axis, each point in the figure is mapped to a point directly across the x-axis from the original point. Therefore, when we reflect a rectangle across the x-axis, the side parallel to the x-axis (in this case, side DC) remains in the same position, while the other side (in this case, side AB) flips and becomes parallel and congruent to side DC. This means that $\triangle DAB' \cong \triangle DCB'$. Since corresponding angles in congruent triangles are congruent, we have $\angle DAB' \cong \angle DCB'$. Therefore, angle $D' = \angle DCB' = \boxed{\text{angle D}}$.
