Maths
What are parallel and perpendicular lines?
Quick answer
Parallel lines run side by side and never meet, always the same distance apart. Perpendicular lines cross or meet at a right angle of exactly 90 degrees.
In one sentence
Parallel lines never meet and stay the same distance apart, while perpendicular lines cross at a right angle.
Explained
Look at railway tracks. The two rails run side by side, keeping the same distance apart for the whole length, and they never meet. These are parallel lines. The wooden sleepers are laid across the rails at right angles. They are perpendicular to the rails.
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Parallel lines go in exactly the same direction. However far you extend them, they never meet. In diagrams, small matching arrows on the lines show they are parallel. In writing, we use the sign ∥.
Perpendicular lines meet, or cross, at a right angle, which is 90 degrees. The corner of a book or a piece of paper is a right angle. A small square marks the corner in diagrams, and the sign is ⟂. See angles.
Both ideas help to describe shapes. A rectangle has two pairs of parallel sides, and all its corners are perpendicular. A trapezium has just one pair of parallel sides. A triangle has none. In a square, each side is parallel to the one opposite and perpendicular to the ones next to it. The shape names are in quadrilaterals.
To check, use a ruler or a set square. Slide a set square along a ruler to draw parallel lines. Fold a piece of paper twice to make a perfect right angle. On a coordinate grid, parallel lines have the same slope, and horizontal and vertical lines are perpendicular. See coordinates.
Not all lines that do not meet are parallel in 3D space, but in flat drawings on a page, lines that never meet are parallel.
Examples
| Where | Parallel | Perpendicular |
|---|---|---|
| Railway | the two rails | the sleepers and the rails |
| Window | top and bottom edges | top and side edges |
| Zebra crossing | the white stripes | stripes and the kerb |
| Letter H | the two upright bars | the bar across and the uprights |
Common mistakes
- Thinking lines must be horizontal to be parallel. Any two lines going the same direction can be parallel, even sloping ones.
- Calling every crossing perpendicular. Only a 90° crossing counts.
- Relying on how it looks. Check using a set square or measure the distance at both ends.
Quick quiz
Parallel and perpendicular lines
Check what you know with 4 quick questions.
Question 1 of 4
What is true of parallel lines?
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Related topics
Angles
An angle measures the amount of turn between two lines that meet at a point. Angles are measured in degrees (°); a right angle is 90° and a full turn is 360°.
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
Coordinates
Coordinates are a pair of numbers that give an exact position on a grid, like (3, 5). The first number is how far across (x) and the second is how far up (y).
Area
Area is the amount of flat space inside a shape, measured in square units like cm² or m². A rectangle 4 cm by 3 cm has an area of 4 × 3 = 12 cm².
Parts of a circle
A circle has a centre, a radius, a diameter and a circumference. The radius runs from the centre to the edge, and the diameter is twice the radius.
Perimeter
Perimeter is the total distance all the way around the outside of a flat shape. For a rectangle 5 cm long and 3 cm wide, it is 5 + 3 + 5 + 3 = 16 cm.