Parallel and perpendicular lines
Two straight lines can do three different things:
- never meet — we call them parallel;
- meet at a right angle — we call them perpendicular;
- meet at any other angle — we just say they intersect (cross).
In Year 4 we mostly care about the first two: parallel and perpendicular.
Parallel lines
Parallel lines stay the same distance apart all the way. They can be far apart or close together, but the gap never changes.
Real-world parallel lines:
- the two rails of a train track
- the lines on writing paper
- the long edges of a ruler
We mark parallel lines with little arrows on each line — two arrows on one pair, three on another pair if there is more than one set in the same picture.
In writing, "line A is parallel to line B" is shortened to A ∥ B with two vertical strokes.
Perpendicular lines
Perpendicular lines meet at a right angle — exactly a quarter turn.
Real-world perpendicular lines:
- the cross in the middle of a window frame
- the corner where a wall meets the floor
- the lines of a "+" sign
We mark a perpendicular meeting with a small square in the corner, the same way we mark any right angle.
The short way to write "perpendicular" is A ⊥ B.
Three ways to test if lines are parallel
- Slide-the-ruler test — put a ruler across both lines and see if it crosses them at the same angle.
- Grid test — on squared paper, parallel lines either go in the same direction along the grid, or rise the same number of squares for every square they go across.
- Distance test — measure the gap between the two lines in two different places. If the gap is the same, the lines are parallel.
Three ways to test if lines are perpendicular
- Square-corner test — slide the corner of a book or a set square against the meeting point. If it fits exactly, the lines are perpendicular.
- Protractor test — measure the angle between them. If it is 90°, they are perpendicular.
- Cross-pattern test — the four angles around the meeting point are all the same size (each is a right angle).
Lines that simply cross
If two lines meet at an angle that is not a right angle, they are still intersecting, but they are neither parallel nor perpendicular. Two roads meeting at a Y-junction are like this.
A worked picture
Imagine a rectangle drawn on the page. Its sides come in two pairs.
- The two long sides are parallel to each other.
- The two short sides are parallel to each other.
- Every long side is perpendicular to every short side.
This is why a rectangle has four right angles — it is built from two pairs of parallel lines meeting perpendicularly.
What's next
- Classifying triangles
- Classifying quadrilaterals — uses parallel sides a lot
- Back to the introduction