Parallel vs. Perpendicular — What's the Difference?

By Tayyaba Rehman — Updated on September 26, 2023
Parallel lines run alongside each other and never intersect; perpendicular lines intersect at a right angle (90 degrees).

Key Differences

Parallel and perpendicular are fundamental concepts in geometry describing the relationships between lines. Parallel lines are those that, regardless of their length, will never intersect, maintaining a constant distance apart due to having the same slope. Conversely, perpendicular lines intersect each other at a right angle, meaning the slopes of the two lines are negative reciprocals of each other.
In analytical geometry, the understanding of parallel and perpendicular lines is crucial for solving numerous problems and understanding spatial relationships. Parallel lines have identical slopes when represented in the slope-intercept form, y = mx + b, where 'm' represents the slope. Perpendicular lines, on the other hand, have slopes that multiply to -1, indicating the characteristic right angle at their intersection.
When visualizing parallel and perpendicular lines in the coordinate plane, parallel lines appear as a set of straight lines running in the same direction without converging, portraying uniformity and balance. Perpendicular lines appear as intersecting lines creating four right angles, embodying a sense of orthogonality and intersection in geometrical shapes and designs.
In real-world applications, the concepts of parallel and perpendicular lines are omnipresent. Parallel lines can be observed in the arrangement of railway tracks and the lanes of a highway, ensuring that the paths never intersect. Perpendicular lines are evident in the corners of buildings and the crossroads of streets, establishing right-angled intersections and structures.

Comparison Chart

Definition

Lines that run alongside each other and never intersect
Lines that intersect each other at a right angle (90 degrees)

Slope

Have identical slopes
Have slopes that are negative reciprocals of each other

Intersection

Never intersect
Always intersect at one point

Representation

Appear as straight lines running in the same direction
Appear as intersecting lines creating four right angles

Real-world Application

Seen in railway tracks and highway lanes
Evident in corners of buildings and crossroads of streets

Compare with Definitions

Parallel

Having the same direction, course, nature, or tendency; corresponding.
The parallel developments in technology have revolutionized multiple industries.

Perpendicular

Intersecting at a right angle.
The two streets are perpendicular, creating a crossroad at the intersection.

Parallel

A person or thing that is similar or analogous to another.
The invention of the internet has a parallel in the invention of the printing press.

Perpendicular

Of a line or plane; being at right angles to another line or plane.
The surface of the table and the edge of the ruler were perpendicular, allowing for accurate measurement.

Parallel

Being an equal distance apart everywhere
Dancers in two parallel rows. See Usage Note at absolute.

Perpendicular

At an angle of 90° to a given line, plane, or surface or to the ground.
The ladder was placed perpendicular to the wall for stability.

Parallel

Of, relating to, or designating two or more straight coplanar lines that do not intersect.

Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects.

Parallel

Of, relating to, or designating two or more planes that do not intersect.

Perpendicular

At an angle of 90° to a given line, plane, or surface or to the ground
Dormers and gables that extend perpendicular to the main roofline

Parallel

Of, relating to, or designating a line and a plane that do not intersect.

Perpendicular

Denoting the latest stage of English Gothic church architecture, prevalent from the late 14th to mid 16th centuries and characterized by broad arches, elaborate fan vaulting, and large windows with vertical tracery
The Perpendicular style
The handsome Perpendicular church of St Andrew

Parallel

Of, relating to, or designating curves or surfaces everywhere equidistant.

Perpendicular

A straight line at an angle of 90° to a given line, plane, or surface
At each division draw a perpendicular representing the surface line

Parallel

Having comparable parts, analogous aspects, or readily recognized similarities
The parallel lives of two contemporaries.

Perpendicular

(Mathematics) Intersecting at or forming right angles.

Parallel

Having the same tendency or direction
Parallel motives and aims.

Perpendicular

Being at right angles to the horizontal; vertical.

Parallel

(Grammar) Having identical or equivalent syntactic constructions in corresponding clauses or phrases.

Perpendicular

Often Perpendicular Of or relating to a style of English Gothic architecture of the 1300s and 1400s, characterized by the use of fan vaulting and broad windows with many mullions.

Parallel

Moving in the same direction at a fixed interval
Parallel motion.
Parallel fifths.

Perpendicular

In a perpendicular position.

Parallel

Having the same tonic. Used of scales and keys
C minor is the parallel minor scale of C major.

Perpendicular

(Mathematics) A line or plane perpendicular to a given line or plane.

Parallel

(Electronics) Denoting a circuit or part of a circuit connected in parallel.

Perpendicular

A perpendicular position.

Parallel

Of or relating to the simultaneous transmission of all the bits of a byte over separate wires
A parallel port.
A parallel interface.

Perpendicular

A device, such as a plumb line, that is used in marking the vertical from a given point.

Parallel

Of or relating to the simultaneous performance of multiple operations
Parallel processing.

Perpendicular

A vertical or nearly vertical line or plane.

Parallel

In a parallel relationship or manner
A road and a railway that run parallel.

Perpendicular

(geometry) At or forming a right angle (to something).
In most houses, the walls are perpendicular to the floor.

Parallel

(Mathematics) One of a set of parallel geometric figures, such as lines or planes.

Perpendicular

Exactly upright; extending in a straight line toward the centre of the earth, etc.

Parallel

One that closely resembles or is analogous to another
A unique event, without parallel in history.

Perpendicular

Independent of or irrelevant to each other; orthogonal.

Parallel

A comparison indicating likeness; an analogy.

Perpendicular

(geometry) A line or plane that is perpendicular to another.

Parallel

The condition of being parallel; near similarity or exact agreement in particulars; parallelism.

Perpendicular

A device such as a plumb line that is used in making or marking a perpendicular line.

Parallel

Any of the imaginary lines representing degrees of latitude that encircle the earth parallel to the plane of the equator.

Perpendicular

A meal eaten at a tavern bar while standing up.

Parallel

(Printing) A sign indicating material referred to in a note or reference.

Perpendicular

Exactly upright or vertical; pointing to the zenith; at right angles to the plane of the horizon; extending in a right line from any point toward the center of the earth.

Parallel

(Electronics) An arrangement of components in a circuit that splits the current into two or more paths. Used chiefly in the phrase in parallel.

Perpendicular

At right angles to a given line or surface; as, the line ad is perpendicular to the line bc.

Parallel

To make or place parallel to something else
Paralleled the ditch to the highway.

Perpendicular

A line at right angles to the plane of the horizon; a vertical line or direction.

Parallel

To be or extend parallel to
A trail that parallels the crater rim.

Perpendicular

A line or plane falling at right angles on another line or surface, or making equal angles with it on each side.

Parallel

To be similar or analogous to
Claimed that fetal development parallels the evolution of the species.

Perpendicular

A straight line at right angles to another line

Parallel

To be or provide an equal for; match.

Perpendicular

A Gothic style in 14th and 15th century England; characterized by vertical lines and a four-centered (Tudor) arch and fan vaulting

Parallel

To show to be analogous; compare or liken
Critics who have paralleled the novel's plot to an ancient myth.

Perpendicular

A cord from which a metal weight is suspended pointing directly to the earth's center of gravity; used to determine the vertical from a given point

Parallel

Equally distant from one another at all points.
The horizontal lines on my notebook paper are parallel.

Perpendicular

An extremely steep face

Parallel

Having the same overall direction; the comparison is indicated with "to".
The two railway lines are parallel.

Perpendicular

Intersecting at or forming right angles;
The axes are perpendicular to each other
Parallel lines never converge
Concentric circles are parallel
Dancers in two parallel rows

Parallel

Either not intersecting, or coinciding.

Perpendicular

At right angles to the plane of the horizon or a base line;
A vertical camera angle
The monument consists of two vertical pillars supporting a horizontal slab
Measure the perpendicular height

Parallel

(computing) Involving the processing of multiple tasks at the same time.
A parallel algorithm

Perpendicular

Extremely steep;
The great perpendicular face of the cliff

Parallel

With a parallel relationship.
The road runs parallel to the canal.

Perpendicular

Denoting the latest English Gothic architectural style of the 14th–16th centuries.
The cathedral was built in the perpendicular style, showcasing elaborate fan vaulting.

Parallel

One of a set of parallel lines.

Perpendicular

Being at right angles to the plane of the horizon; upright.
The post was perfectly perpendicular, not leaning in any direction.

Parallel

Direction conformable to that of another line.

Parallel

A line of latitude.
The 31st parallel passes through the center of my town.

Parallel

An arrangement of electrical components such that a current flows along two or more paths; see in parallel.

Parallel

Something identical or similar in essential respects.

Parallel

A comparison made; elaborate tracing of similarity.
Johnson's parallel between Dryden and Pope

Parallel

(military) One of a series of long trenches constructed before a besieged fortress, by the besieging force, as a cover for troops supporting the attacking batteries. They are roughly parallel to the line of outer defenses of the fortress.

Parallel

(printing) A character consisting of two parallel vertical lines, used in the text to direct attention to a similarly marked note in the margin or at the foot of a page.

Parallel

To construct or place something parallel to something else.

Parallel

Of a path etc: To be parallel to something else.

Parallel

Of a process etc: To be analogous to something else.

Parallel

To compare or liken something to something else.

Parallel

To make to conform to something else in character, motive, aim, etc.

Parallel

To equal; to match; to correspond to.

Parallel

To produce or adduce as a parallel.

Parallel

Extended in the same direction, and in all parts equally distant; as, parallel lines; parallel planes.
Revolutions . . . parallel to the equinoctial.

Parallel

Having the same direction or tendency; running side by side; being in accordance (with); tending to the same result; - used with to and with.
When honor runs parallel with the laws of God and our country, it can not be too much cherished.

Parallel

Continuing a resemblance through many particulars; applicable in all essential parts; like; similar; as, a parallel case; a parallel passage.

Parallel

A line which, throughout its whole extent, is equidistant from another line; a parallel line, a parallel plane, etc.
Who made the spider parallels design,Sure as De Moivre, without rule or line ?

Parallel

Direction conformable to that of another line,
Lines that from their parallel decline.

Parallel

Conformity continued through many particulars or in all essential points; resemblance; similarity.
Twixt earthly females and the moonAll parallels exactly run.

Parallel

A comparison made; elaborate tracing of similarity; as, Johnson's parallel between Dryden and Pope.

Parallel

Anything equal to, or resembling, another in all essential particulars; a counterpart.
None but thyself can be thy parallel.

Parallel

One of the imaginary circles on the surface of the earth, parallel to the equator, marking the latitude; also, the corresponding line on a globe or map; as, the counry was divided into North and South at the 38th parallel.

Parallel

One of a series of long trenches constructed before a besieged fortress, by the besieging force, as a cover for troops supporting the attacking batteries. They are roughly parallel to the line of outer defenses of the fortress.

Parallel

A character consisting of two parallel vertical lines (thus, ) used in the text to direct attention to a similarly marked note in the margin or at the foot of a page.

Parallel

That arrangement of an electrical system in which all positive poles, electrodes, terminals, etc., are joined to one conductor, and all negative poles, etc., to another conductor; - called also multiple. Opposed to series.

Parallel

To place or set so as to be parallel; to place so as to be parallel to, or to conform in direction with, something else.
The needle . . . doth parallel and place itself upon the true meridian.

Parallel

Fig.: To make to conform to something else in character, motive, aim, or the like.
His life is paralleledEven with the stroke and line of his great justice.

Parallel

To equal; to match; to correspond to.

Parallel

To produce or adduce as a parallel.
My young remembrance can not parallelA fellow to it.

Parallel

To be parallel; to correspond; to be like.

Parallel

Something having the property of being analogous to something else

Parallel

An imaginary line around the Earth parallel to the equator

Parallel

Be parallel to;
Their roles are paralleled by ours

Parallel

Make or place parallel to something;
They paralleled the ditch to the highway

Parallel

Duplicate or match;
The polished surface twinned his face and chest in reverse

Parallel

Being everywhere equidistant and not intersecting;
Parallel lines never converge
Concentric circles are parallel
Dancers in two parallel rows
The axes are perpendicular to each other

Parallel

Of or relating to the simultaneous performance of multiple operations;
Parallel processing

Parallel

Denoting lines that run alongside each other and never intersect.
The parallel lines on the notebook paper serve as a guide for handwriting.

Parallel

Extending in the same direction and being equidistant at all points.
The two parallel roads run between the hills, never meeting each other.

Parallel

A relationship of mutual resemblance or correspondence between two objects.
The parallel between the two novels is striking, suggesting an influence of one author on the other.

Common Curiosities

What does parallel mean in geometry?

In geometry, parallel refers to lines that run alongside each other and never intersect.

What does perpendicular mean in geometry?

In geometry, perpendicular refers to lines that intersect each other at a right angle (90 degrees).

At what angle do perpendicular lines intersect?

Perpendicular lines intersect at a right angle, which is 90 degrees.

How can you identify parallel lines on a graph?

On a graph, parallel lines can be identified as they have the same slope and different y-intercepts.

How are the slopes of perpendicular lines related?

The slopes of perpendicular lines are negative reciprocals of each other.

Where can you observe perpendicular lines in the real world?

Perpendicular lines can be observed in the corners of buildings and at street intersections.

Can parallel lines ever meet?

No, parallel lines, by definition, will never meet or intersect each other.

Where can you see examples of parallel lines in real life?

Examples of parallel lines in real life include railway tracks and lanes on a highway.

How are parallel and perpendicular lines used in construction?

Parallel and perpendicular lines are essential in construction for creating structures with balanced, symmetrical, and right-angled designs.

Can curved lines be parallel or perpendicular?

Yes, curved lines can be parallel or perpendicular if they maintain a constant distance (parallel) or intersect at right angles (perpendicular) at the point of tangency.

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