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.
Oh, I am studying quadrilaterals, specifically I am on Chapter 5 proving a quadrilateral is a Parallelogram, Claire.
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...