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 ∥
perpendicular ⊥
intersecting
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.
