In a plane, if a transversal is perpendicular to one of two parallel lines, what is true about its relation to the other line?

In a plane, if a transversal is perpendicular to one of two parallel lines, what is true about its relation to the other line?

• A. It is parallel to the other line
• B. It is perpendicular to the other line
• C. It intersects at a right angle only if lines are vertical
• D. It is perpendicular to one line and not the other

Answer: (B)

Key idea: a line perpendicular to one of two parallel lines is perpendicular to the other as well. Two parallel lines share the same direction, so a line that cuts one at a right angle must also cut the other at a right angle. The 90-degree angle with one line transfers to the parallel line because the directions of the two lines are the same. This means the transversal forms right angles with both lines. The orientation of the lines (vertical, horizontal, etc.) doesn’t change this relationship. So the transversal is perpendicular to the other line as well.

Key idea: a line perpendicular to one of two parallel lines is perpendicular to the other as well.

Two parallel lines share the same direction, so a line that cuts one at a right angle must also cut the other at a right angle. The 90-degree angle with one line transfers to the parallel line because the directions of the two lines are the same. This means the transversal forms right angles with both lines. The orientation of the lines (vertical, horizontal, etc.) doesn’t change this relationship. So the transversal is perpendicular to the other line as well.