Question

planes x and y intersect at a right angle. ab and cg lie in plane x and do not intersect. rs lies in plane y. which statements are true? select three options. ab and cg are parallel. ab and rs are parallel. cg and rs are perpendicular. ab and rs must intersect. cg lies in plane x. rs lies in plane x.

Explanation:

Step1: Analyze parallel lines

Since $\overleftrightarrow{AB}$ and $\overleftrightarrow{CG}$ lie in plane $X$ and do not intersect, by the definition of parallel lines (two lines in the same plane that do not intersect), $\overleftrightarrow{AB}\parallel\overleftrightarrow{CG}$.

Step2: Analyze perpendicular lines

Planes $X$ and $Y$ intersect at a right - angle. $\overleftrightarrow{CG}$ lies in plane $X$ and $\overleftrightarrow{RS}$ lies in plane $Y$. When two planes are perpendicular, a line in one plane perpendicular to the line of intersection of the two planes is perpendicular to any line in the other plane that is parallel to the line of intersection. Here, $\overleftrightarrow{CG}$ (in plane $X$) and $\overleftrightarrow{RS}$ (in plane $Y$) are perpendicular.

Step3: Check line - plane relationship

The problem states that $\overleftrightarrow{AB}$ and $\overleftrightarrow{CG}$ lie in plane $X$. So, by the given information, $\overleftrightarrow{CG}\subset$ plane $X$.

$\overleftrightarrow{AB}$ and $\overleftrightarrow{RS}$ are not parallel because they are in perpendicular planes. $\overleftrightarrow{AB}$ and $\overleftrightarrow{RS}$ do not have to intersect as they are in different planes. $\overleftrightarrow{RS}$ lies in plane $Y$ (not plane $X$).

Answer:

• $\overleftrightarrow{AB}$ and $\overleftrightarrow{CG}$ are parallel
• $\overleftrightarrow{CG}$ and $\overleftrightarrow{RS}$ are perpendicular
• $\overleftrightarrow{CG}$ lies in plane $X$