Two groups of parallelograms with parallel opposite sides are called parallelograms. Parallelogram is generally named by the graphic name followed by four vertices. Note: When using letters to represent quadrangles, be sure to indicate whether the vertices are clockwise or counterclockwise.

Two groups of parallelograms with parallel opposite sides are parallelograms (definition judgment method).

A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

Two sets of quadrilaterals with equal opposite sides are parallelograms.

Two groups of quadrangles with equal diagonal angles are parallelograms (two groups of opposite sides are judged to be parallel).

Quadrilaterals whose diagonals bisect each other are parallelograms.

The area of a parallelogram is twice the area of a triangle formed by one of its diagonals.

The area of parallelogram is also equal to the cross product of two adjacent edge vectors.

Any line passing through the midpoint of the parallelogram divides the area in two.

Any nondegenerate affine transformation adopts parallelogram.

The rotational symmetry order of parallelogram is 2 (to 180) (if it is a square, it is 4). If it also has two lines of reflection symmetry, it must be a diamond or a rectangle (non-right-angled rectangle). If it has four symmetrical reflection lines, it is a square.

The perimeter of a parallelogram is 2(a+b), where a and b are the lengths of adjacent sides.