What does the parallel lines theorem say about vertical lines?

What does the parallel lines theorem say about vertical lines?

• A. Any two vertical lines are parallel
• B. Vertical lines are never parallel
• C. Vertical lines are perpendicular to the x-axis
• D. Vertical lines have a slope of 1

Answer: (A)

Vertical lines run straight up and down, so they share the same direction. All distinct vertical lines do not meet each other, which means they are parallel. In slope terms, the slope of a vertical line is undefined, but that doesn’t stop every vertical line from being parallel to every other vertical line. So the statement that any two vertical lines are parallel captures this idea clearly. The other options mix in different relationships (perpendicular to the x-axis, or a specific slope) that aren’t what the parallel lines idea is about.

Vertical lines run straight up and down, so they share the same direction. All distinct vertical lines do not meet each other, which means they are parallel. In slope terms, the slope of a vertical line is undefined, but that doesn’t stop every vertical line from being parallel to every other vertical line. So the statement that any two vertical lines are parallel captures this idea clearly. The other options mix in different relationships (perpendicular to the x-axis, or a specific slope) that aren’t what the parallel lines idea is about.