Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. which two statements are both true? \\(\boldsymbol{\overleftrightarrow{de} \perp \overleftrightarrow{hb}}\\) and \\(\boldsymbol{\overleftrightarrow{ac} \parallel \overleftrightarrow{fg}}\\) \\(\boldsymbol{\overleftrightarrow{ac} \perp \overleftrightarrow{hb}}\\) and \\(\boldsymbol{\overleftrightarrow{ac} \parallel \overleftrightarrow{fg}}\\) \\(\boldsymbol{\overleftrightarrow{hb} \perp \overleftrightarrow{fg}}\\) and \\(\boldsymbol{\overleftrightarrow{hb} \perp \overleftrightarrow{de}}\\) \\(\boldsymbol{\overleftrightarrow{ac} \parallel \overleftrightarrow{fg}}\\) and \\(\boldsymbol{\overleftrightarrow{de} \parallel \overleftrightarrow{ac}}\\)

Explanation:

1. Analyze the first option: $\overleftrightarrow{DE} \perp \overleftrightarrow{HB}$? From the diagram, $\overleftrightarrow{DE}$ and $\overleftrightarrow{HB}$ do not form a right angle. So this statement is false.
2. Analyze the second option: $\overleftrightarrow{AC} \perp \overleftrightarrow{HB}$? The diagram shows a right angle between $\overleftrightarrow{AC}$ and $\overleftrightarrow{HB}$, so $\overleftrightarrow{AC} \perp \overleftrightarrow{HB}$ is true. Also, $\overleftrightarrow{AC} \parallel \overleftrightarrow{FG}$? The arrows and the diagram suggest they are parallel, so this statement is also true.
3. Analyze the third option: $\overleftrightarrow{HB} \perp \overleftrightarrow{FG}$? From the diagram, $\overleftrightarrow{HB}$ and $\overleftrightarrow{FG}$ do not form a right angle. So this statement is false.
4. Analyze the fourth option: $\overleftrightarrow{DE} \parallel \overleftrightarrow{AC}$? From the diagram, $\overleftrightarrow{DE}$ and $\overleftrightarrow{AC}$ are not parallel (their directions and intersections suggest otherwise). So this statement is false.

Answer:

B. $\overleftrightarrow{AC} \perp \overleftrightarrow{HB}$ and $\overleftrightarrow{AC} \parallel \overleftrightarrow{FG}$