Parallel Lines: Definition, Examples, Chart, and Practice

What are parallel lines?

Parallel lines are lines that go in the same direction and never meet.

They stay the same distance apart, even if you imagine the lines continuing forever.

In drawings, lines often have arrows on the ends. The arrows remind us that a line keeps going.

Parallel lines rule

Use this rule when you check a pair of lines.

Parallel lines have the same direction and never cross.

If two lines would meet or cross, they are not parallel.

Parallel lines chart

This chart compares parallel lines with lines that are not parallel.

Parallel lines do not have to be horizontal. They can be vertical or slanted too, as long as they keep the same direction.

In later geometry, the same pair of parallel lines can help explain transversals and parallel lines, then corresponding angles.

How to spot parallel lines

Step 1: Look at the direction of both lines.

Step 2: Imagine the lines going on forever.

Step 3: Ask: would they ever meet?

If the answer is no, and the lines stay the same distance apart, the lines are parallel.

Worked example

Problem: A rectangle has four sides. Which sides are parallel?

Step 1: Look at the top and bottom sides. They go in the same direction and do not meet.

Step 2: Look at the left and right sides. They also go in the same direction and do not meet.

Answer: A rectangle has two pairs of parallel sides.

Parallel sides in shapes

Many shapes have parallel sides.

A rectangle has two pairs of parallel sides. A square also has two pairs of parallel sides.

A parallelogram has opposite sides that are parallel. Some trapezoids have one pair of parallel sides.

Parallel line marks

A diagram may use matching arrow marks to show that two lines or two sides are parallel.

If two sides have the same arrow mark, that tells you the sides are parallel.

Different diagrams may use one arrow, two arrows, or small matching marks. The key idea is that matching marks show matching direction.

Real-life parallel lines

Notebook lines are usually parallel. Road lane lines are often parallel. Railroad tracks look parallel because the rails stay side by side.

You can also find parallel lines on window blinds, shelves, floor tiles, fences, and the opposite sides of many picture frames.

Parallel vs. perpendicular

Parallel lines never meet. Perpendicular lines do meet, and they make a right angle where they cross.

This is a common mix-up. If two lines cross, they are not parallel.

If two lines cross at exactly 90°, they are perpendicular.

Common mistakes

Do not call lines parallel just because they are close together. They must stay the same distance apart.

Do not call line segments parallel if they point in different directions. If the full lines would meet, they are not parallel.

Do not forget that vertical lines can be parallel too. Parallel lines do not have to be flat across the page.

Quick practice

1. The top and bottom sides of a rectangle are parallel.

2. Two lines that cross are not parallel.

3. Two vertical lines that stay side by side are parallel.

4. Railroad rails are a real-life example of parallel lines.

5. Lines that meet at a square corner are perpendicular, not parallel.