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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. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean Parallel Postulate and neither condition can be proven without appealing to the Euclidean Parallel Postulate or one of its equivalent formulations. The three-dimensional counterpart of a parallelogram is a parallelepiped.

The etymology (in Greek παραλληλ-όγραμμον, a shape "of parallel lines") reflects the definition.

A simple (non self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true:12

Two pairs of opposite sides are equal in length.

Two pairs of opposite angles are equal in measure.

The diagonals bisect each other.

One pair of opposite sides are parallel and equal in length.

Adjacent angles are supplementary.

Each diagonal divides the quadrilateral into two congruent triangles.

The sum of the squares of the sides equals the sum of the squares of the diagonals. (This is the parallelogram law.)

It has rotational symmetry of order 2.
What are you studying Jane?
Oh, I am studying quadrilaterals, specifically I am on Chapter 5 proving a quadrilateral is a Parallelogram, Claire.
by david faustino December 18, 2012
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any quadrilateral, such as a square, rectangle or rhombus, with opposing parallel sides being of equal length

Usage: Words such as parallelogram, square, rectangle, rhombus, parallel, equal and length, all well-defined in any proper dictionary, are, as Urban Dictionary entries, misplaced and of minimal benefit.
by Scott Fairbairn September 03, 2008
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A group of four or more paraplegics.

They tend to roam around eateries and fat people, taunting them by going faster than them even without usable legs.
Dude, let me in!

There's a parallelogram after me!

Hide the Ho-ho's!
by Xildra October 18, 2009
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A word that only appears int he lyrics to one song- Motörhead by hawkwind, and then again by Motörhead.
Fourth day, five day marathon,
We're moving like a parallelogram
Don't move, the morning's not a pretty sight
I guess I'll see you all on the ice
I should be tired and all I am is wired
ain't felt this good for an hour
Motorhead, remember me now,
Motorhead, all night...
by Gumba Gumba August 03, 2004
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If you make an illuminati triangle with two hands, then flip one hand. This is what you end up with.

The {illuminati} is in 4 sided shapes too.
Person 2: Well, you just...
by BurningToast May 29, 2018
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the physical posture of someone that's crippled, usually marked by their leaning slouch to one side, as noted by a vertical parallelogram.
John: "Holy shit a parallelogram messaged me on myspace."
Joe: "You gonna hit it?"
John: "Probably."
by crippy August 19, 2009
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