Question

identify all pairs of parallel and perpendicular lines in the image below. ○ $overleftrightarrow{cd}perpoverleftrightarrow{ef},overleftrightarrow{ef}perpoverleftrightarrow{ab},overleftrightarrow{ab}perpoverleftrightarrow{gh},overleftrightarrow{ef}paralleloverleftrightarrow{ij}$ ○ $overleftrightarrow{cd}perpoverleftrightarrow{ef},overleftrightarrow{cd}perpoverleftrightarrow{ij},overleftrightarrow{ab}perpoverleftrightarrow{gh},overleftrightarrow{ef}paralleloverleftrightarrow{ij}$ ○ $overleftrightarrow{cd}perpoverleftrightarrow{ef},overleftrightarrow{cd}perpoverleftrightarrow{ij},overleftrightarrow{ab}perpoverleftrightarrow{gh},overleftrightarrow{ef}paralleloverleftrightarrow{ij},overleftrightarrow{ef}paralleloverleftrightarrow{gh},overleftrightarrow{gh}paralleloverleftrightarrow{ij}$

Explanation:

Step1: Recall line - relationship definitions

Parallel lines never intersect and perpendicular lines intersect at a 90 - degree angle.

Step2: Analyze perpendicular lines

We can see that $\overleftrightarrow{CD}\perp\overleftrightarrow{EF}$ and $\overleftrightarrow{CD}\perp\overleftrightarrow{IJ}$ because of the right - angle symbols. Also, $\overleftrightarrow{AB}\perp\overleftrightarrow{GH}$ as they intersect at right angles.

Step3: Analyze parallel lines

$\overleftrightarrow{EF}\parallel\overleftrightarrow{IJ}$ and $\overleftrightarrow{EF}\parallel\overleftrightarrow{GH}$ and $\overleftrightarrow{GH}\parallel\overleftrightarrow{IJ}$ since they are straight lines that do not intersect.

Answer:

$\overleftrightarrow{CD}\perp\overleftrightarrow{EF},\overleftrightarrow{CD}\perp\overleftrightarrow{IJ},\overleftrightarrow{AB}\perp\overleftrightarrow{GH},\overleftrightarrow{EF}\parallel\overleftrightarrow{IJ},\overleftrightarrow{EF}\parallel\overleftrightarrow{GH},\overleftrightarrow{GH}\parallel\overleftrightarrow{IJ}$