Question

which statement about the image below is false?
○ $overleftrightarrow{ab}perpoverleftrightarrow{ef}$
○ $overleftrightarrow{ab}perpoverleftrightarrow{cd}$
○ $overleftrightarrow{ef}paralleloverleftrightarrow{cd}$
○ $overleftrightarrow{cd}perpoverleftrightarrow{ef}$

Explanation:

Step1: Recall perpendicular and parallel definitions

Perpendicular lines form 90 - degree angles, parallel lines never intersect.

Step2: Analyze the image

In the image, $\overleftrightarrow{AB}$ is perpendicular to $\overleftrightarrow{EF}$ and $\overleftrightarrow{CD}$, and $\overleftrightarrow{EF}\parallel\overleftrightarrow{CD}$.

Step3: Evaluate each option

• $\overleftrightarrow{AB}\perp\overleftrightarrow{EF}$ is true as there are right - angle markings.
• $\overleftrightarrow{AB}\perp\overleftrightarrow{CD}$ is true as there are right - angle markings.
• $\overleftrightarrow{EF}\parallel\overleftrightarrow{CD}$ is true as they are vertical and non - intersecting.
• $\overleftrightarrow{CD}\perp\overleftrightarrow{EF}$ is false since they are parallel.

Answer:

$\overleftrightarrow{CD}\perp\overleftrightarrow{EF}$