Parallelogram vs. Square — What's the Difference?
By Tayyaba Rehman & Maham Liaqat — Updated on April 3, 2024
A square is a specific type of parallelogram with equal sides and angles, whereas a parallelogram has opposite sides parallel and equal.
Difference Between Parallelogram and Square
Table of Contents
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Key Differences
A parallelogram is a four-sided polygon (quadrilateral) characterized by opposite sides being parallel and equal in length. In contrast, a square is a special case of a parallelogram where all four sides are of equal length, and all angles are equal to 90 degrees. This distinction highlights the square's more stringent requirements compared to the general criteria for a parallelogram.
While the interior angles in a parallelogram must add up to 360 degrees, with opposite angles being equal, a square takes this a step further by having all four interior angles exactly equal, each measuring 90 degrees. This equality of angles is what makes a square not only a parallelogram but also a rectangle and a rhombus, showcasing its unique position in the hierarchy of quadrilaterals.
In terms of symmetry, both parallelograms and squares have lines of symmetry, but the square has four lines of symmetry due to its equal sides and angles, compared to the parallelogram, which typically has two. This aspect of symmetry in squares contributes to its balance and uniformity, making it a figure of equal proportion from every angle.
The diagonal properties of these two shapes also differ significantly. In a parallelogram, diagonals bisect each other but are not necessarily equal in length and do not necessarily bisect the angles. In a square, however, the diagonals are equal in length, bisect each other at right angles, and also bisect the angles of the square, reflecting its more restrictive and defined nature.
Regarding their geometric applications, both shapes are used extensively in various fields, including architecture, engineering, and design. However, the properties of a square—such as its uniformity and symmetry—make it particularly useful in situations requiring standardization and equal measurements, whereas parallelograms are often utilized in more complex designs and structures where varied angles and lengths are needed.
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Comparison Chart
Sides
Opposite sides parallel and equal
All sides equal and parallel
Angles
Opposite angles equal
All angles equal to 90 degrees
Diagonals
Bisect each other, not necessarily equal
Equal in length, bisect at right angles
Symmetry
At least one line of symmetry
Four lines of symmetry
Use Cases
Complex designs, architecture
Standardization, calculations
Interior Angle Sum
360 degrees
360 degrees
Lines of Symmetry
Typically two
Four
Diagonal Properties
Do not bisect angles at 90 degrees
Bisect angles at 90 degrees
Application in Fields
Engineering, design
Architecture, engineering, design
Specificity
Less restrictive, more general
More restrictive, special case
Compare with Definitions
Parallelogram
A quadrilateral with opposite sides parallel and equal.
Architects use the shape of a parallelogram to create interesting roof designs.
Square
Symbol of fairness and equality.
The square's equal sides and angles make it a symbol of balance in design.
Parallelogram
Appears in various orientations.
Parallelograms are used in art to create a sense of movement and balance.
Square
A parallelogram with four equal sides and angles.
The square tiles evenly covered the kitchen floor.
Parallelogram
Can have unequal angles and sides, except for the opposites.
A parallelogram's flexible properties make it versatile in design.
Square
Represents uniformity and simplicity.
The square shape of the garden made it easy to divide into equal parts.
Parallelogram
Used in complex geometric calculations.
Calculating the area of a parallelogram requires the base and height.
Square
Foundational in geometry and mathematics.
Learning about squares is essential in understanding the properties of shapes.
Parallelogram
Diagonals bisect each other but aren't equal.
The diagonals of a parallelogram intersect at their midpoints.
Square
Diagonals are equal and bisect each other at right angles.
The square's diagonals divided it into four symmetrical triangles.
Parallelogram
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Square
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or 100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length.
Parallelogram
A four-sided plane figure with opposite sides parallel.
Square
A plane figure with four equal straight sides and four right angles
A grid of ruled squares
Parallelogram
(geometry) A convex quadrilateral in which each pair of opposite edges are parallel and of equal length.
Square
An open, typically four-sided, area surrounded by buildings in a village, town, or city
A market square
Leicester Square
Parallelogram
Either of two rectangular areas (respectively the large parallelogram and the small parallelogram) abutting the goal line in front of the goal. (Since 1986 officially named the large rectangle and small rectangle, though the older names are still occasionally used.)
Square
The product of a number multiplied by itself
A circle's area is proportional to the square of its radius
Parallelogram
A right-lined quadrilateral figure, whose opposite sides are parallel, and consequently equal; - sometimes restricted in popular usage to a rectangle, or quadrilateral figure which is longer than it is broad, and with right angles.
Square
An L-shaped or T-shaped instrument used for obtaining or testing right angles
A carpenter's square
Parallelogram
A quadrilateral whose opposite sides are both parallel and equal in length
Square
A person considered to be old-fashioned or boringly conventional in attitude or behaviour
Reg is such a square
Square
A square meal
Three squares a day
Square
Having the shape or approximate shape of a square
A square table
Square
Denoting a unit of measurement equal to the area of a square whose side is of the unit specified
30,000 square feet of new gallery space
Square
At right angles; perpendicular
These lines must be square to the top and bottom marked edges
Square
Level or parallel
Place two pieces of wood one on top of the other, ensuring that they are exactly square
Square
(of two people) owing nothing to each other
An acknowledgement that we are square
Square
Old-fashioned or boringly conventional
Elvis was anything but square
Square
(of rhythm) simple and straightforward.
Square
Directly; straight
The ball hit me square in the forehead
Square
In a direction transversely across the field or pitch
The ball bounced almost square to the left
Square
Make square or rectangular; give a square or rectangular cross section to
You can square off the other edge
Square
Multiply (a number) by itself
5 squared equals 25
Square
Make compatible; reconcile
I'm able to square my profession with my religious beliefs
Square
Balance (an account)
Institutions are anxious to square their books before the election
Square
Bring (one's shoulders) into a position in which they appear square and broad, typically to prepare oneself for a difficult task or event
Chin up, shoulders squared, she stepped into the room
Square
Secure the help or acquiescence of (someone), especially by offering an inducement
Trying to square the press
Square
Pass (a ball) across the field, especially towards the centre.
Square
Set (a yard or other part of a ship) at right angles to the keel or other point of reference.
Square
(of a planet) have a square aspect with (another planet or position)
Saturn squares the Sun on the 17th
Square
A polygon having four equal sides and four equal angles.
Square
Something having an equal-sided rectangular form
A square of cloth.
Square
A T-shaped or L-shaped instrument for drawing or testing right angles.
Square
(Mathematics) The product obtained when a number or quantity is multiplied by itself
49 is the square of 7.
Square
(Games) Any of the quadrilateral spaces on a board, as in chess.
Square
Abbr. Sq. An open, usually four-sided area at the intersection of two or more streets, often planted with grass and trees for use as a park.
Square
A rectangular space enclosed by streets and occupied by buildings; a block.
Square
The flower bud of a cotton plant, with three bracts surrounding the unopened flower in a pyramidal structure.
Square
(Slang) A person who is regarded as dull, rigidly conventional, and out of touch with current trends.
Square
Having four equal sides and four right angles.
Square
Forming a right angle.
Square
In alignment or flush
Put the paper square with the edge of the desk.
Square
Abbr. sq. Expressed in units measuring area
Square feet.
Square
Having a specified length in each of two equal dimensions
A room that is 12 feet square.
Square
Having a base that is a square
A square pyramid.
Square
(Nautical) Set at right angles to the mast and keel. Used of the yards of a square-rigged ship.
Square
Approximately rectangular and equilateral in cross section
A square house.
Square
Characterized by blocklike solidity or sturdiness.
Square
Honest; direct
A square answer.
Square
Just; equitable
A square deal.
Square
Having all accounts settled; even
I paid what I owed you, so we're square.
Square
(Sports) Even; tied.
Square
(Slang) Rigidly conventional; dull.
Square
To cut to a square or rectangular shape. Often used with off.
Square
To test or adjust for conformity to a desired plane, straight line, or right angle.
Square
To mark into squares. Often used with off.
Square
To bring into conformity or agreement
She could not square the request with her principles.
Square
To bring (oneself) into a better position or relation
He tried to square himself with his parents.
Square
To set straight or at approximate right angles
Square one's cap.
Square
To bring into balance; settle
Square a debt.
Square
(Sports) To even the score of
To square a game.
Square
To raise (a number or quantity) to the second power.
Square
To find a square equal in area to (the area of a given figure).
Square
(Informal) To bribe or fix
A party in litigation that tried to square the judge.
Square
(Mathematics) To be at right angles.
Square
To agree or conform
A story that doesn't square with the facts.
Square
(Mathematics) At right angles.
Square
In a square shape.
Square
In a solid manner; firmly.
Square
Directly; straight
Ran square into each other.
Square
In an honest, straightforward manner.
Square
(geometry) A polygon with four sides of equal length and four right angles; an equilateral rectangle; a regular quadrilateral.
Square
Something characterized by a square, or nearly square, form.
Square
A cell in a grid.
You may not move a piece to a square already occupied by one of your own pieces.
Square
A square piece, part, or surface.
A square of glass
Square
The front of a woman's dress over the bosom, usually worked or embroidered.
Square
(North America) A dessert cut into rectangular pieces, or a piece of such a dessert.
Square
(printing) A certain number of lines, forming a portion of a column, nearly square; used chiefly in reckoning the prices of advertisements in newspapers.
Column inch
Square
An L- or T-shaped tool used to place objects or draw lines at right angles.
Square
A true measure, standard, or pattern.
Square
An open space or park, often in the center of a town, not necessarily square in shape, often containing trees, seating and other features pleasing to the eye.
Square
A street surrounding a public square or plaza.
Square
(mathematics) The product of a number or quantity multiplied by itself; the second power of a number, value, term or expression.
64 is the square of 8.
Square
(military formation) A body of troops drawn up in a square formation.
Square
A socially conventional or conservative person; a person who has little or no interest in the latest fads or trends: still sometimes used in modern terminology.
Why do you always wear a tie? Don't be such a square!
Square
(British) The symbol # on a telephone; hash.
Enter your account number followed by a square.
Square
(cricket) The central area of a cricket field, with one or more pitches of which only one is used at a time.
An ideal playing area is roughly circular in shape with a central area, the cricket square, measuring 27.44 metres by 27.44 metres and boundaries 45.75 metres from the sides of the square.
Square
(real estate) A unit of measurement of area, equal to a 10 foot by 10 foot square, i.e. 100 square feet or roughly 9.3 square metres. Used in real estate for the size of a house or its rooms, though progressively being replaced by square metres in metric countries such as Australia.
Square
(roofing) A unit used in measuring roof area equivalent to 100 square feet (9.29 m²) of roof area. The materials for roofing jobs are often billed by the square in the United States.
Square
(academia) A mortarboard.
Square
Senseid|en|square meal elliptically}} {{ellipsis of square meal
Even when times were tough, we got three squares a day.
Square
(archaic) Exact proportion; justness of workmanship and conduct; regularity; rule.
Square
The relation of harmony, or exact agreement; equality; level.
Square
(astrology) The position of planets distant ninety degrees from each other; a quadrate.
Square
(dated) The act of squaring, or quarrelling; a quarrel.
Square
(slang) Cigarette.
Square
(brewing) A vat used for fermentation.
Square
A well-defined core of a human body, a flat section from the fundament to the thoracic diaphragm.
Square
Shaped like a square the polygon.
Square
Forming a right angle (90°).
A square corner
Square
(of box-shaped objects such as buildings or metal frames) Forming right angles in all planes as intended; not rack or leaning.
The foundation has to be level and the framing has to be square.
Square
(nautical) Forming right angles with the mast or the keel, and parallel to the horizon; said of the yards of a square-rigged vessel when they are so braced.
Square
Used in the names of units of area formed by multiplying a unit of length by itself.
Square metre
Square mile
Square
Honest; straightforward; fair.
I'm just looking for a square deal on my car repair.
Square dealing
Square
Satisfied; comfortable with; not experiencing any conflict.
Square
Even; tied
To make or leave the accounts square
The sides were square at the end of the half.
Square
Socially conventional; boring.
Square
(cricket) In line with the batsman's popping crease.
Square
Solid, decent, substantial.
It may be prison, but at least I'm getting three square meals a day.
Square
Having a shape broad for the height, with angular rather than curving outlines.
A man of a square frame
Square
Directly.
Square
(transitive) To adjust so as to align with or place at a right angle to something else; in particular:
The casting was mounted on a milling machine so that its sides could be squared.
Square
(nautical) To place at a right angle to the mast or keel.
To square the yards
Square
(rowing) To rotate the oars so that they are perpendicular to the water.
Square
(ambitransitive) To resolve or reconcile; to suit or fit.
John can square this question up for us.
These results just don't square with what we expected.
Square
(transitive) To adjust or adapt so as to bring into harmony with something.
I cannot square the results of the experiment with my hypothesis.
To square our actions by the opinions of others
Square
Of a value, term, or expression, to multiply by itself; to raise to the second power.
Square
To draw, with a pair of compasses and a straightedge only, a square with the same area as.
Square the circle
Square
To tile (completely fill) with squares.
Square
(soccer) To make a short low pass sideways across the pitch
Square
(archaic) To take opposing sides; to quarrel.
Square
To accord or agree exactly; to be consistent with; to suit; to fit.
Square
(obsolete) To go to opposite sides; to take an attitude of offense or defense, or of defiance; to quarrel.
Square
To take a boxing attitude; often with up or off.
Square
To form with four sides and four right angles.
Square
To form with right angles and straight lines, or flat surfaces.
To square mason's work
Square
To compare with, or reduce to, any given measure or standard.
Square
(astrology) To hold a quartile position respecting.
Square
The corner, or angle, of a figure.
Square
Hence, anything which is square, or nearly so
He bolted his food down his capacious throat in squares of three inches.
Square
A pane of glass.
Square
An area of four sides, generally with houses on each side; sometimes, a solid block of houses; also, an open place or area for public use, as at the meeting or intersection of two or more streets.
The statue of Alexander VII. stands in the large square of the town.
Square
An instrument having at least one right angle and two or more straight edges, used to lay out or test square work. It is of several forms, as the T square, the carpenter's square, the try-square., etc.
Square
Hence, a pattern or rule.
Square
The product of a number or quantity multiplied by itself; thus, 64 is the square of 8, for 8
Square
Exact proportion; justness of workmanship and conduct; regularity; rule.
They of Galatia [were] much more out of square.
I have not kept my square.
Square
A body of troops formed in a square, esp. one formed to resist a charge of cavalry; a squadron.
Square
Fig.: The relation of harmony, or exact agreement; equality; level.
We live not on the square with such as these.
Square
The position of planets distant ninety degrees from each other; a quadrate.
Square
The act of squaring, or quarreling; a quarrel.
Square
The front of a woman's dress over the bosom, usually worked or embroidered.
Square
Having four equal sides and four right angles; as, a square figure.
Square
Forming a right angle; as, a square corner.
Square
Having a shape broad for the height, with rectilineal and angular rather than curving outlines; as, a man of a square frame.
Square
Exactly suitable or correspondent; true; just.
She's a most triumphant lady, if report be square to her.
Square
Rendering equal justice; exact; fair; honest; as, square dealing.
Square
Even; leaving no balance; as, to make or leave the accounts square.
Square
Leaving nothing; hearty; vigorous.
By Heaven, square eaters.More meat, I say.
Square
At right angles with the mast or the keel, and parallel to the horizon; - said of the yards of a square-rigged vessel when they are so braced.
Square
To form with four equal sides and four right angles.
Square
To form with right angles and straight lines, or flat surfaces; as, to square masons' work.
Square
To compare with, or reduce to, any given measure or standard.
Square
To adjust; to regulate; to mold; to shape; to fit; as, to square our actions by the opinions of others.
Square my trialTo my proportioned strength.
Square
To make even, so as to leave no remainder or difference; to balance; as, to square accounts.
Square
To multiply by itself; as, to square a number or a quantity.
Square
To hold a quartile position respecting.
The icy Goat and Crab that square the Scales.
Square
To place at right angles with the keel; as, to square the yards.
Square
To accord or agree exactly; to be consistent with; to conform or agree; to suit; to fit.
No works shall find acceptance . . .That square not truly with the Scripture plan.
Square
To go to opposite sides; to take an attitude of offense or defense, or of defiance; to quarrel.
Are you such foolsTo square for this?
Square
To take a boxing attitude; - often with up, sometimes with off.
Square
(geometry) a plane rectangle with four equal sides and four right angles; a four-sided regular polygon;
You can compute the area of a square if you know the length of its sides
Square
The product of two equal terms;
Nine is the second power of three
Gravity is inversely proportional to the square of the distance
Square
An open area at the meeting of two or more streets
Square
Something approximating the shape of a square
Square
Someone who doesn't understand what is going on
Square
A formal and conservative person with old-fashioned views
Square
Any artifact having a shape similar to a plane geometric figure with four equal sides and four right angles;
A checkerboard has 64 squares
Square
A hand tool consisting of two straight arms at right angles; used to construct or test right angles;
The carpenter who built this room must have lost his square
Square
Raise to the second power
Square
Make square;
Square the circle
Square the wood with a file
Square
Cause to match, as of ideas or acts
Square
Position so as to be square;
He squared his shoulders
Square
Be compatible with;
One idea squares with another
Square
Pay someone and settle a debt;
I squared with him
Square
Turn the paddle; in canoeing
Square
Turn the oar, while rowing
Square
Having four equal sides and four right angles or forming a right angle;
A square peg in a round hole
A square corner
Square
Leaving no balance;
My account with you is now all square
Square
Characterized by honesty and fairness;
A square deal
Wanted to do the square thing
Square
Without evasion or compromise;
A square contradiction
He is not being as straightforward as it appears
Square
Rigidly conventional or old-fashioned
Square
In a straight direct way;
Looked him squarely in the eye
Ran square into me
Square
With honesty and fairness;
Dealt squarely with his customers
Always treated me square
Square
In a square shape;
A squarely cut piece of paper
Folded the sheet of paper square
Square
Firmly and solidly;
Hit the ball squarely
The bat met the ball squarely
Planted his great bulk square before his enemy
Common Curiosities
Can all parallelograms be considered squares?
No, only those parallelograms with all sides and angles equal can be considered squares.
Are there any parallelograms with right angles that aren't squares?
Yes, rectangles are parallelograms with right angles but unequal adjacent sides, distinguishing them from squares.
How do the diagonals of a square and parallelogram differ?
Square diagonals are equal, bisect at right angles, and bisect the angles of the square, unlike those of a general parallelogram.
Can a parallelogram have four right angles?
Yes, but if a parallelogram has four right angles, it is also a rectangle and possibly a square if all sides are equal.
What makes a square different from other parallelograms?
A square has all sides and angles equal, making it a special case of a parallelogram with additional restrictions.
Why is a square considered a perfect shape?
Its equal sides, angles, and symmetrical properties make it a model of balance and uniformity.
How do you calculate the area of a square and a parallelogram?
The area of a square is found by squaring the length of one side, while a parallelogram's area is the base length times the height.
How does the symmetry of a square benefit its use in design?
Its symmetry makes it ideal for creating patterns, tessellations, and facilitating easy calculation and replication.
Can the properties of a square be applied to three-dimensional shapes?
Yes, squares are the faces of cubes, applying their properties to three-dimensional space and structures.
What is the significance of a square in mathematics?
Squares are fundamental in geometry, representing uniformity, and are key in algebra through squaring numbers.
What kind of symmetry does a parallelogram have?
A parallelogram typically has bilateral symmetry, with one or two lines of symmetry depending on its specific shape.
Is it possible for a parallelogram to have curved sides?
No, by definition, a parallelogram must have straight, parallel opposite sides.
Why are squares used so frequently in everyday measurements?
Their uniform dimensions make calculations straightforward, ideal for floor plans, tiling, and more.
Do squares have more structural stability than other parallelograms?
Yes, the equal length of sides and right angles in squares often result in structures with greater stability.
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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.
Co-written by
Maham Liaqat
