Question

Two distinct lines, I and m, are each perpendicular to the same line, n. Select all the true statements.

A) Lines I and m are perpendicular.
B) Lines I and n are parallel.
C) Lines m and n are perpendicular.
D) Lines I and n are perpendicular.

Answer 1

Lines I and m are parallel to each other since they are both perpendicular to line n. Lines I and n as well as m and n are perpendicular, each forming a 90° angle with line n.

Step-by-step explanation:

If two distinct lines, I and m, are each perpendicular to the same line n, then we can draw the following conclusions about their relationships:

• Lines I and m are not necessarily perpendicular to each other, but they are parallel to each other. This is because if two lines are both perpendicular to a third line, then they run in the same direction and do not intersect.
• Lines I and n are perpendicular, forming a 90° angle between each other.
• Similarly, lines m and n are also perpendicular, again forming a 90° angle between each other.
  

Based on the options given:

• A) Lines I and m are perpendicular - This is not true; they are parallel to one another.
• B) Lines I and n are parallel - This is incorrect; they are perpendicular.
• C) Lines m and n are perpendicular - This is true.
• D) Lines I and n are perpendicular - This is also true.