Question

the movement of the progress bar may be uneven because questions can be worth more or less
which two statements are both true?
\\( \overleftrightarrow { f g } \perp \overleftrightarrow { h b } \\) and \\( \overleftrightarrow { f g } || \overleftrightarrow { d e } \\)
\\( \overleftrightarrow { f g } || \overleftrightarrow { d e } \\) and \\( \overleftrightarrow { d e } || \overleftrightarrow { a c } \\)
\\( \overleftrightarrow { h b } \perp \overleftrightarrow { a c } \\) and \\( \overleftrightarrow { f g } || \overleftrightarrow { d e } \\)
\\( \overleftrightarrow { f g } \perp \overleftrightarrow { h b } \\) and \\( \overleftrightarrow { a c } \perp \overleftrightarrow { h b } \\)

Explanation:

Step1: Analyze perpendicularity

From the diagram, $\overleftrightarrow{FG}$ and $\overleftrightarrow{HB}$ form a right angle (marked by the square), so $\overleftrightarrow{FG} \perp \overleftrightarrow{HB}$. Also, $\overleftrightarrow{AC}$ and $\overleftrightarrow{HB}$: since $\overleftrightarrow{FG} \parallel \overleftrightarrow{AC}$ (they have the same slope/are parallel) and $\overleftrightarrow{FG} \perp \overleftrightarrow{HB}$, then $\overleftrightarrow{AC} \perp \overleftrightarrow{HB}$.

Step2: Check other options

• First option: $\overleftrightarrow{FG} \parallel \overleftrightarrow{DE}$? No, $\overleftrightarrow{FG}$ and $\overleftrightarrow{DE}$ are not parallel (different directions).
• Second option: $\overleftrightarrow{DE} \parallel \overleftrightarrow{AC}$? No, they are not parallel.
• Third option: $\overleftrightarrow{HB} \perp \overleftrightarrow{AC}$? Wait, but $\overleftrightarrow{FG} \parallel \overleftrightarrow{DE}$? No, $\overleftrightarrow{FG}$ and $\overleftrightarrow{DE}$ are not parallel.
• Fourth option: $\overleftrightarrow{FG} \perp \overleftrightarrow{HB}$ (true) and $\overleftrightarrow{AC} \perp \overleftrightarrow{HB}$ (true) as explained.

Answer:

$\overleftrightarrow{FG} \perp \overleftrightarrow{HB}$ and $\overleftrightarrow{AC} \perp \overleftrightarrow{HB}$ (the last option)