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

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# Brief Explanations:
1. For " $\overleftrightarrow{AB}$ and $\overleftrightarrow{CG}$ are parallel": In plane $ X $, two lines that don't intersect are parallel, and $ \overleftrightarrow{AB} $ and $ \overleftrightarrow{CG} $ lie in plane $ X $ and don't intersect, so this is true.
2. For " $\overleftrightarrow{CG}$ and $\overleftrightarrow{RS}$ are perpendicular": Planes $ X $ and $ Y $ are perpendicular, $ \overleftrightarrow{CG} $ is in plane $ X $ (vertical) and $ \overleftrightarrow{RS} $ is in plane $ Y $ (horizontal, along the intersection), so they are perpendicular, this is true.
3. For " $\overleftrightarrow{CG}$ lies in plane $ X $": From the diagram and description, $ \overleftrightarrow{CG} $ is in plane $ X $, this is true.

The other statements: $ \overleftrightarrow{AB} $ and $ \overleftrightarrow{RS} $ are not parallel (different planes, one vertical one horizontal), they don't have to intersect (skew lines), and $ \overleftrightarrow{RS} $ lies in plane $ Y $, not $ X $.
# Answer:
- $ \boldsymbol{\overleftrightarrow{AB}} $ and $ \boldsymbol{\overleftrightarrow{CG}} $ are parallel.
- $ \boldsymbol{\overleftrightarrow{CG}} $ and $ \boldsymbol{\overleftrightarrow{RS}} $ are perpendicular.
- $ \boldsymbol{\overleftrightarrow{CG}} $ lies in plane $ X $.

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