Question

planes x and y are perpendicular. points a, e, f, and g are points only in plane x. points r and s are points in both planes x and y. lines ea and fg are parallel. based on this information, which pair of lines, together, could be perpendicular to \\(\overline{rs}\\)? select two options. \\(\square \overleftrightarrow{ea}\\) \\(\square \overleftrightarrow{er}\\) \\(\square \overleftrightarrow{ef}\\) \\(\square \overleftrightarrow{fg}\\) \\(\square \overleftrightarrow{fs}\\)

Explanation:

1. $\overline{RS}$ lies on the intersection of perpendicular planes X and Y, so it is along the line where the two planes meet.
2. A line perpendicular to $\overline{RS}$ in this 3D setup must be either perpendicular to it within plane X or plane Y.
3. $\overleftrightarrow{EA}$ and $\overleftrightarrow{FG}$ are parallel lines in plane X, and from the diagram, they are oriented perpendicular to $\overline{RS}$.
4. $\overleftrightarrow{ER}$ lies along $\overline{RS}$ in plane Y, so it is not perpendicular. $\overleftrightarrow{EF}$ is parallel to $\overline{RS}$ in plane X, so it is not perpendicular. $\overleftrightarrow{FS}$ is perpendicular to $\overline{RS}$ but only one such line is needed, and the question asks for a pair that together could be perpendicular, which matches the parallel lines EA and FG.

Answer:

$\square$ $\overleftrightarrow{EA}$
$\square$ $\overleftrightarrow{FG}$