What does perpendicular mean? Two lines, edges or surfaces are perpendicular when they meet or cross at a right angle, which is exactly 90 degrees, like the corner of a square or the plus sign. The word can also mean standing perfectly upright, straight up and down.
Geometry lessons are its home ground, though carpenters, designers, surveyors and historians of medieval buildings rely on it as well. This guide gives the perpendicular meaning in plain words, the maths rules, everyday examples, the difference from parallel, and a little history.
Entry at a glance
Meaning
At a right angle (90 degrees) to a given line or plane; also, exactly verticalPart of speech
Adjective; also a noun (a perpendicular line)Pronunciation
pur-puhn-DIK-yuh-lerSymbol
⊥, as in AB ⊥ CD (AB is perpendicular to CD)Word forms
perpendicularly (adverb), perpendicularity (noun)Origin
Late Latin perpendicularis, from perpendiculum, a plumb lineRelated ideas
right angle, orthogonal, normal (in geometry), vertical
What does perpendicular mean in maths and daily life?
- At a right angle. One line, edge or surface meets another at 90 degrees. The two streets are perpendicular. Draw a line perpendicular to the base.
- Exactly upright. Rising straight up from level ground: a perpendicular cliff, a perpendicular climb. Here it overlaps with vertical.
- As a noun. A perpendicular is a line at right angles to another: drop a perpendicular from the top corner to the base.
Note that perpendicular lines do not have to be vertical and horizontal. Turn a plus sign on its side to make an X: the lines are still perpendicular as long as the angle between them is 90 degrees. So if a classmate asks what is the meaning of perpendicular, answer with the angle, not the direction.
Perpendicular lines in geometry
In school geometry, a few rules come up again and again:
- Perpendicular lines form four right angles where they cross.
- The symbol is ⊥, and a small square drawn in the corner of a diagram marks a right angle.
- On a graph, two lines are perpendicular when their slopes multiply to -1. If one line has slope 2, a perpendicular line has slope -1/2. (A vertical line and a horizontal line are also perpendicular, even though a vertical slope is undefined.)
- A perpendicular bisector cuts a line segment into two equal halves at a right angle.
- The shortest distance from a point to a line is along the perpendicular.
Parallel vs perpendicular
| Feature | Parallel | Perpendicular |
|---|---|---|
| Do they meet? | Never, they stay the same distance apart | Yes, they cross or touch |
| Angle | No angle between them | Exactly 90 degrees |
| Slopes on a graph | Equal | Multiply to -1 |
| Symbol | ∥ | ⊥ |
| Everyday example | railway tracks | the corner of a book |
A quick way to remember: the letters ll in parallel look like two parallel lines, and the capital letter T looks like two perpendicular ones.
Perpendicular examples around you
- The legs of a well-made table are perpendicular to the tabletop.
- On many city grids, avenues run perpendicular to cross streets.
- A wall should be perpendicular to the floor, or doors will not close properly.
- For homework, Meera had to list every pair of perpendicular edges on a shoebox.
- The climbers faced an almost perpendicular rock face for the last hundred metres.
- Park your bike perpendicular to the kerb so it does not block the path.
Word origin and a style of building
Perpendicular comes from Late Latin perpendicularis, "vertical, as a plumb line", from perpendiculum, a plumb line, the weighted string builders hang to find true vertical. That came from perpendere, "to weigh carefully" (per-, thoroughly, plus pendere, to hang or weigh). So the first idea was a line hanging straight down. English used the word in the 15th century for a line at right angles to the horizon, and by the 16th century for a line at right angles to any other line. Check what is the definition of perpendicular in a geometry book today, and that later sense is the answer.
With a capital P, Perpendicular is also the name of the last phase of English Gothic architecture, from the late 14th to the early 16th century, known for tall, straight vertical lines in its windows and wall panels.
Close words and common errors
- Vertical means straight up and down relative to the ground. Perpendicular means at right angles to some other line, whatever its direction.
- Orthogonal is a technical word for perpendicular used in higher maths, statistics and computing.
- Normal in geometry and physics means a line perpendicular to a surface.
- Spelling. It ends in -cular, like particular, not "-culer".
Related science words on this site include congruent and density; the science vocabulary list gathers many others.
Frequently asked questions
Perpendicular definition for beginners: what is it?
Perpendicular means meeting at a perfect right angle, like the two lines of a plus sign. It can also mean standing straight up.
How do you define perpendicular lines?
Perpendicular lines are two lines that cross or meet at an angle of exactly 90 degrees. They form four right angles where they cross.
Are perpendicular lines always vertical and horizontal?
No. Any two lines meeting at 90 degrees are perpendicular, whatever way they point. A vertical and a horizontal line are just the most familiar example.
How does a perpendicular slope work?
A perpendicular slope is the negative reciprocal of another line's slope. Flip the fraction and change its sign: the perpendicular to slope 4 is -1/4.
Is perpendicular the same as vertical?
Not exactly. Vertical always means up and down relative to the ground. Perpendicular means at right angles to some other line, and only means upright when that other line is level.
How do you pronounce perpendicular?
Say pur-puhn-DIK-yuh-ler, with the main stress on DIK. It has five syllables.