Question

$\overline{ab}$ is parallel to $\overline{xy}$. $\overline{ab}$ and $\overline{xy}$ are reflected over the $x-$axis to form $\overline{ab}$ and $\overline{xy}$. complete the statement: $\overline{ab}$ is …… to $\overline{xy}$
show your work here
\bigcirc parallel \qquad \bigcirc perpendicular
\bigcirc congruent \qquad \bigcirc none of the above

Explanation:

Step1: Recall Reflection Properties

Reflection over the x - axis is a rigid transformation. Rigid transformations (like reflection) preserve the shape and orientation of lines in terms of parallelism. If two lines are parallel, reflecting them over the same line (the x - axis here) will result in two new lines that are also parallel.

Step2: Apply to Given Segments

We know that \(\overline{AB}\parallel\overline{XY}\). When we reflect \(\overline{AB}\) to get \(\overline{A'B'}\) and \(\overline{XY}\) to get \(\overline{X'Y'}\) over the x - axis, the transformation does not change the angle between the original lines (since it's a rigid transformation). Since the original lines were parallel, the reflected lines will also be parallel.

Answer:

A. parallel