Question

Lines m and n are parallel. line p is perpendicular to both line m and line n. Which statement about lines m, n, and p is not always true?

1) Line m and line n are perpendicular
2) Line m and line n are parallel
3) Line m and line p are perpendicular
4) Line n and line p are perpendicular

Answer 1

The statement that line m and line n are perpendicular is not true because parallel lines do not intersect at right angles; they are always equidistant from each other. The perpendicular line p is at right angles to both lines m and n, making statements 2, 3, and 4 true.

Step-by-step explanation:

The question involves understanding the relationships between parallel and perpendicular lines. If lines m and n are parallel, then they will never intersect. The fact that line p is perpendicular to both lines m and n means that it intersects both lines at right angles (90 degrees). Considering these relationships, we can determine which statements are always true and which one is not.

1. Line m and line n are perpendicular - This statement is not true. Parallel lines are always the same distance apart and do not intersect, much less at a right angle.
2. Line m and line n are parallel – This statement is true, as given by the question.
3. Line m and line p are perpendicular – This statement is true, based on the condition that p is perpendicular to m.
4. Line n and line p are perpendicular – This statement is true, because p is stated to be perpendicular to n as well.