Lines that never meet

The idea

Parallel lines are a pair of lines that lie on the same plane and never meet, however far they are extended at both ends.

Along the track

Look at the two rails of a straight railway track, or the two long edges of a ruler. They run side by side.

Imagine the two lines going on and on, in both directions. Would they ever meet?

• Yes, far away they meet
• No, never
• They meet at one end only

Zoom out

Here are three pairs of lines. Zoom out to look farther along each pair, at both ends, and see what it does.

Parallel lines

One pair never meets: its lines run the same way, so the gap between them stays the same. The other two pairs lean towards each other, so far away they meet, one to the right and one to the left.

Parallel lines are a pair of lines that lie on the same plane and do not meet, however far we extend them at both ends.

• Pair | Far away
• Pair 1 | Never meet
• Pair 2 | Meet, to the right
• Pair 3 | Meet, to the left

Notes

Parallel lines are a pair of lines that lie on the same plane and do not meet, however far we extend them at both ends.

Check yourself

Two lines on a page do not meet anywhere on the page. Are they parallel?

Two lines do not meet on the right, but they meet far away on the left. Are they parallel?

Which of these is a pair of parallel lines?

How many points do two parallel lines have in common?

• Yes. They do not meet, so they are parallel.. They may meet just beyond the page, as Pair 2 and Pair 3 did.
• We cannot say yet. Parallel lines must not meet however far we extend them. — correct. Yes! Pair 2 and Pair 3 did not meet on the page either. They met only far away.
• No. Parallel lines must meet somewhere.. Parallel lines never meet. The question is whether these two ever do.
• Yes. They do not meet on the right.. We must look at both ends. They meet on the left, so they are not parallel.
• No. Meeting at either end means they are not parallel. — correct. Yes! We must extend the lines at both ends. One meeting point is enough.
• Yes. The meeting point is very far away.. However far away it is, lines that meet are not parallel.
• The two rails of a straight railway track — correct. Yes! The rails run the same way and never meet.
• Two roads that meet at a crossing. They meet at the crossing, so they are not parallel.
• The two hands of a clock at 3:00. The hands meet at the centre of the clock, so they are not parallel.
• One, where they would meet. Parallel lines never meet, so there is no such point.
• Two, one at each end. Parallel lines never meet at either end.
• None, because they never meet — correct. Yes! If they had a point in common, they would meet there.