Question

question 1
which two statements are both true?
○ $overleftrightarrow{hb}perpoverleftrightarrow{ac}$ and $overleftrightarrow{fg}paralleloverleftrightarrow{de}$
○ $overleftrightarrow{fg}perpoverleftrightarrow{hb}$ and $overleftrightarrow{fg}paralleloverleftrightarrow{de}$
○ $overleftrightarrow{fg}paralleloverleftrightarrow{de}$ and $overleftrightarrow{de}paralleloverleftrightarrow{ac}$
○ $overleftrightarrow{fg}perpoverleftrightarrow{hb}$ and $overleftrightarrow{ac}perpoverleftrightarrow{hb}$

Explanation:

Step1: Recall parallel and perpendicular line - segment properties

Parallel lines have the same slope and never intersect. Perpendicular lines intersect at a 90 - degree angle.

Step2: Analyze each option

• Option 1: Check if $\overleftrightarrow{HB}\perp\overleftrightarrow{AC}$ and $\overleftrightarrow{FG}\parallel\overleftrightarrow{DE}$. There is no indication of $\overleftrightarrow{HB}\perp\overleftrightarrow{AC}$ from the figure.
• Option 2: Check if $\overleftrightarrow{FG}\perp\overleftrightarrow{HB}$ and $\overleftrightarrow{FG}\parallel\overleftrightarrow{DE}$. There is no indication of $\overleftrightarrow{FG}\perp\overleftrightarrow{HB}$ from the figure.
• Option 3: Check if $\overleftrightarrow{FG}\parallel\overleftrightarrow{DE}$ and $\overleftrightarrow{DE}\parallel\overleftrightarrow{AC}$. From the figure, it appears that $\overleftrightarrow{FG}$, $\overleftrightarrow{DE}$ and $\overleftrightarrow{AC}$ are all parallel to each other.
• Option 4: Check if $\overleftrightarrow{FG}\perp\overleftrightarrow{HB}$ and $\overleftrightarrow{AC}\perp\overleftrightarrow{HB}$. There is no indication of $\overleftrightarrow{FG}\perp\overleftrightarrow{HB}$ from the figure.

Answer:

$\overleftrightarrow{FG}\parallel\overleftrightarrow{DE}$ and $\overleftrightarrow{DE}\parallel\overleftrightarrow{AC}$