Two groups of parallelograms with parallel opposite sides are parallelograms.

Two sets of quadrilaterals with equal opposite sides are parallelograms.

Two sets of quadrangles with equal diagonals are parallelograms.

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

The opposite sides and diagonals of a parallelogram are equal.

Diagonal lines of parallelograms are equally divided.

A parallelogram is a figure with a symmetrical center, and the symmetrical center is the focus of two diagonal lines.

A quadrilateral with three right angles is a rectangle.

A parallelogram with right angles is a rectangle.

Diagonal lines of rectangles are equal.

A quadrilateral with four equilateral sides is a diamond.

A set of parallelograms with equal adjacent sides is a diamond.

Diagonal lines of the diamond are perpendicular to each other and bisect each diagonal line.

A set of rectangles with equal adjacent sides is a square.

One of the angles is a right angle.

A set of parallelograms with equal adjacent sides and a right angle is a square.

The base angles of an isosceles trapezoid are equal (equilateral and equiangular).

And midline theorem