Definition and properties of parallelogram;
The two sides of the (1) parallelogram are parallel and equal.
(2) The two diagonal lines of a parallelogram are equally divided (rhombus and square)
(3) The diagonals of the parallelogram are equal, and the two adjacent angles are complementary.
(4) The graph obtained by connecting the midpoints of any quadrilateral side is a parallelogram. (inference)
(5) The area of a parallelogram is equal to the product of the base and the height (it can be regarded as a rectangle).
(6) A parallelogram is a rotationally symmetric figure, and the center of rotation is the intersection of two diagonals.
(7) Divide the parallelogram into two congruent figures through the straight line at the diagonal intersection of the parallelogram.
(8) A parallelogram is a central symmetric figure, and the center of symmetry is the intersection of two diagonals.
(9) The general parallelogram is not an axisymmetric figure, and the rhombus is an axisymmetric figure.
(10) In the parallelogram ABCD, AC and BD are diagonals of the parallelogram ABCD, so the sum of squares of four sides is equal to the sum of squares of diagonals (which can be proved by cosine theorem).
(1 1) The diagonal of the parallelogram divides the area of the parallelogram into four parts.
Judge:
(1) Two groups of quadrangles with equal opposite sides are parallelograms;
(2) The quadrilateral whose diagonal lines bisect each other is a parallelogram;
(3) A group of quadrilaterals with parallel and equal opposite sides are parallelograms;
(4) Two groups of parallelograms with parallel opposite sides are parallelograms;
(5) Two groups of quadrangles with equal diagonal are parallelograms;
(6) A group of quadrilaterals with parallel opposite sides and bisected diagonals are parallelograms;
(7) A group of quadrangles with parallel opposite sides and equal diagonals are parallelograms;