Two groups of parallelograms with parallel opposite sides are parallelograms.

Two sets of diagonally equal quadrilaterals are parallelograms.

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

Quadrilaterals whose diagonals bisect each other are parallelograms.

The diamond is a quadrilateral with four equal sides, which belongs to a special parallelogram. In addition to the properties of these graphs, it also has the following properties:

Diagonal lines vertically bisect each other;

All four sides are equal;

Diagonal angles are equal and adjacent angles are complementary;

Each diagonal bisects a set of diagonal lines.

Judge:

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

Parallelograms with diagonal lines perpendicular to each other are diamonds.

A quadrilateral with four equilateral sides is a diamond.

The quadrilateral obtained by connecting the midpoints of the sides of the quadrilateral in turn is called the midpoint quadrilateral. No matter how the shape of the original quadrangle changes, the shape of the midpoint quadrangle is always a parallelogram. The midpoint quadrangle of a diamond is a rectangle.

Diamond area: divided by two or multiplied by height after diagonal multiplication;

The circumference of a diamond is four times the length of its side;

The midpoint of each side connecting the diamonds in turn is a rectangle.

A square is a special kind of diamond.

Trapezoid refers to a set of quadrilaterals whose opposite sides are parallel and the other set of opposite sides are not parallel. Two parallel sides are called the bottom of the trapezoid, and the long side is called the bottom; Non-parallel edges are called waist; The distance between the two bases is called the height of the trapezoid. A trapezoid with a waist perpendicular to the bottom is called a right-angled trapezoid, and two trapezoid with equal waist are called isosceles trapezoid.

The nature and judgment of trapezoid;

One set of quadrilaterals with parallel opposite sides and another set of quadrilaterals with non-parallel opposite sides are trapezoid, but it is difficult to judge that the other set of opposite sides are not parallel. Generally, it is judged that a group of quadrilaterals with parallel and unequal opposite sides are trapezoidal.

The volume calculation formula of trapezoid:

V =[s 1+S2+ radical sign (S 1 * S2)]/3 * h

Note: v: volume; S 1: upper surface area; S2: lower surface area; H: high.

The area formula of trapezoid is: "Upper bottom plus lower bottom times height divided by 2".

Rectangle: a parallelogram with right angles is called a rectangle, that is, a rectangle.

A rectangle has the following properties:

1. The four names of the rectangle are right angles.

2. The diagonals of the rectangle are equal and equally divided.