Topics · Primary Maths · Parallel & Perpendicular
Parallel and perpendicular lines
Both describe a pair of lines, not a single one. Parallel lines run the same way and never meet, however far you follow them. Perpendicular lines cross at a right angle.
- 246 exam papers analysed
- appears in 63% of P6 Maths papers
- ~3 min read
01 One line is never parallel
This is the first thing to fix. Parallel and perpendicular are not properties a line can have on its own — they always describe how two lines sit relative to each other. A single line drawn on a page is neither.
So the question is never “is this line parallel?” It is always “is this line parallel to that one?”
02 Parallel: the test
Two lines are parallel if the gap between them never changes. Follow them as far as you like and they stay exactly as far apart.
Which gives you a way to check a drawing that a ruler can settle: measure the gap in two different places. Same both times, parallel. Different, not.
The pair below looks near enough parallel over the length drawn. Carry the lines on, though, and the gap closes — so they are not.
03 Perpendicular: the test
Two lines are perpendicular if they meet at a right angle — exactly 90°. The corner of a piece of paper or a set square held into the join settles it.
They do not have to cross in the middle, and they do not both have to be upright or flat. A line leaning at 30° and another at 120° are perpendicular, because the angle between them is 90°.
Perpendicular lines meet. Parallel lines never do. That alone tells you which word a question wants.
04 Where they turn up in shapes
Most marks on this topic are not won on a bare pair of lines — they are won inside a shape, because several shapes are defined by these relationships.
- A trapezium has exactly one pair of parallel sides. That pair is what makes it a trapezium.
- A parallelogram has two pairs — the name says it.
- A rectangle and a square have both: two pairs of parallel sides, and every pair of neighbouring sides perpendicular.
- In a rhombus the sides are parallel in pairs, and it is the two diagonals that are perpendicular to each other.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- parallelsayPA-ruh-lel
Two lines running in the same direction, always the same distance apart, never meeting however far they are extended. Marked with matching arrows.
- perpendicularsaypur-pen-DIK-yuh-luh
Two lines that meet or cross at a right angle, 90°. Marked with a small square where they join.
- right anglesayRITE ANG-guhlmore than oneright angles
Exactly 90°, a quarter turn. Perpendicular is the word for two lines that make one.
- set squaresaySET skwairmore than oneset squares
The flat triangular tool with a 90° corner, used to draw perpendicular lines and to check whether two lines are perpendicular.
- intersectsayIN-tuh-sekt
To cross or meet. Perpendicular lines intersect at 90°; parallel lines never intersect at all.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P3
Spotting parallel and perpendicular lines in drawings and in the world around.
Practise P3 Parallel & Perpendicular — 10 questions →39% of P3 papers
- P4
Drawing them with a ruler and set square, and naming them in shapes.
Practise P4 Parallel & Perpendicular — 10 questions →41% of P4 papers
- P5
Using them to identify shapes, and describing sides of a figure by these relationships.
Practise P5 Parallel & Perpendicular — 10 questions →20% of P5 papers
- P6
Composite figures, where knowing which sides are parallel or perpendicular is what unlocks a missing length or angle.
Practise P6 Parallel & Perpendicular — 10 questions →63% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“This line is parallel.”
Parallel to what? Both words describe a pair of lines. One line on its own is neither parallel nor perpendicular.
“Parallel lines have to be the same length.”
Length has nothing to do with it. A 2 cm line and a 20 cm line are parallel if they run the same way — a trapezium's parallel sides are usually different lengths.
“They look parallel, so they are.”
Papers say “not drawn to scale” for a reason. Measure the gap in two places, or follow the lines further and see whether it closes.
“Perpendicular means one line is upright and the other is flat.”
It means the angle between them is 90°, whatever direction either one points. A pair leaning at 30° and 120° is perpendicular.
“Parallel lines meet a long way away.”
They never meet. That is the definition, and it is what the word is for — lines that eventually meet are simply not parallel.
Now try it
40 questions across 4 levels, marked as you go with the working shown.