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).
Difference Between Parallel and Perpendicular
Table of Contents
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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)
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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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Written by
Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.
