Martin drew a pair of perpendicular lines and a pair of parallel lines.

Which of these statements best compares the pairs of perpendicular and parallel lines?
Answer
A: Perpendicular and parallel lines always have a common endpoint.

B: Perpendicular and parallel lines have their lines extending in one direction only.

C: Perpendicular lines are lines that intersect at right angles, and parallel lines are lines that never meet.

D: Perpendicular lines have only one point lying on them and parallel lines have no points lying on them.

The correct answer is C: Perpendicular lines are lines that intersect at right angles, and parallel lines are lines that never meet.

To find the correct answer, we need to understand the definitions of perpendicular and parallel lines.

Perpendicular lines are lines that intersect at a right angle (90 degrees). This means that they form a square corner when they meet.

Parallel lines, on the other hand, are lines that never meet, no matter how far they are extended. They stay the same distance apart from each other at all points.

Let's analyze each of the given statements:

A: Perpendicular and parallel lines always have a common endpoint.
This statement is incorrect. Perpendicular lines do not have a common endpoint, but they intersect at a right angle. Parallel lines also do not have a common endpoint, but they never intersect.

B: Perpendicular and parallel lines have their lines extending in one direction only.
This statement is incorrect. Perpendicular lines extend in two different directions from the point of intersection, forming a right angle. Parallel lines, however, extend in the same direction and never meet.

C: Perpendicular lines are lines that intersect at right angles, and parallel lines are lines that never meet.
This statement correctly compares perpendicular and parallel lines. Perpendicular lines intersect at right angles, forming a square corner. Parallel lines never meet and always stay the same distance apart.

D: Perpendicular lines have only one point lying on them and parallel lines have no points lying on them.
This statement is incorrect. Both perpendicular and parallel lines have infinite points lying on them. Perpendicular lines have infinite points on both lines that intersect at right angles, and parallel lines have infinite points along their length.

Based on this analysis, the correct answer is: C) Perpendicular lines are lines that intersect at right angles, and parallel lines are lines that never meet.

Joey plots a point P on the line AB, as shown.




Which statement is true?

Check the definitions of perpendicular and parallel -- and tell us what you think.