Question

practice question 1.6.2
two distinct lines, l and m, are each perpendicular to the same line n.
select all the true statements.
(select all that apply.)
lines l and m are perpendicular
lines l and n are perpendicular.
lines m and n are perpendicular.
lines l and m are parallel
lines l and n are parallel
lines m and n are parallel

Explanation:

1. Recall the properties of perpendicular and parallel lines: If two distinct lines are both perpendicular to the same line, they are parallel to each other. Also, by definition, if a line is perpendicular to another line, that relationship holds.

• For "Lines \( l \) and \( n \) are perpendicular": Given that \( l \) is perpendicular to \( n \), this is true.
• For "Lines \( m \) and \( n \) are perpendicular": Given that \( m \) is perpendicular to \( n \), this is true.
• For "Lines \( l \) and \( m \) are parallel": Since both \( l \) and \( m \) are perpendicular to \( n \), by the theorem "If two lines are perpendicular to the same line, then they are parallel to each other" (in a plane), this is true.
• For "Lines \( l \) and \( m \) are perpendicular": This is false because two lines perpendicular to the same line are parallel, not perpendicular.
• For "Lines \( l \) and \( n \) are parallel": This is false because \( l \) is perpendicular to \( n \), not parallel.
• For "Lines \( m \) and \( n \) are parallel": This is false because \( m \) is perpendicular to \( n \), not parallel.

Answer:

B. Lines \( l \) and \( n \) are perpendicular.
C. Lines \( m \) and \( n \) are perpendicular.
D. Lines \( l \) and \( m \) are parallel.