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 rs? select two options.

Explanation:

Step1: Recall perpendicular - line properties

If a line is in a plane and another line is the intersection of two perpendicular planes, then lines in one plane can be perpendicular to the line of intersection if they are perpendicular to the intersection - line's projection in that plane. Since planes \(X\) and \(Y\) are perpendicular and \(RS\) lies in both planes (intersection of \(X\) and \(Y\)), lines in plane \(X\) that are perpendicular to the direction of \(RS\) in plane \(X\) will be perpendicular to \(RS\).

Step2: Analyze the given lines

Lines \(EA\) and \(FG\) are parallel and lie in plane \(X\). If a line in plane \(X\) is perpendicular to the direction of \(RS\) (which is the intersection of planes \(X\) and \(Y\)), it will be perpendicular to \(RS\). Lines \(EA\) and \(FG\) can be perpendicular to \(RS\) because they are in plane \(X\) and can be oriented in a way to be perpendicular to \(RS\).

Answer:

EA, FG