Question

which statement about the image below is false?
o \stackrel{\leftrightarrow}{cd}\perp\stackrel{\leftrightarrow}{ef}
o \stackrel{\leftrightarrow}{ef}\parallel\stackrel{\leftrightarrow}{cd}
o \stackrel{\leftrightarrow}{ab}\perp\stackrel{\leftrightarrow}{cd}
o \stackrel{\leftrightarrow}{ab}\perp\stackrel{\leftrightarrow}{ef}

Explanation:

Step1: Recall parallel and perpendicular line definitions

Parallel lines never intersect. Perpendicular lines intersect at a right - angle (\(90^{\circ}\)).

Step2: Analyze each option

• For \(\overleftrightarrow{EF}\parallel\overleftrightarrow{CD}\): Lines \(EF\) and \(CD\) are both vertical. Vertical lines are parallel.
• For \(\overleftrightarrow{AB}\perp\overleftrightarrow{CD}\): Line \(AB\) is horizontal and \(CD\) is vertical. Horizontal and vertical lines intersect at \(90^{\circ}\), so they are perpendicular.
• For \(\overleftrightarrow{AB}\perp\overleftrightarrow{EF}\): Line \(AB\) is horizontal and \(EF\) is vertical. Horizontal and vertical lines intersect at \(90^{\circ}\), so they are perpendicular.
• For \(\overleftrightarrow{CD}\perp\overleftrightarrow{EF}\): Since \(CD\parallel EF\) (both vertical), they cannot be perpendicular.

Answer:

\(\overleftrightarrow{CD}\perp\overleftrightarrow{EF}\) is the false statement.