Definition of various special quadrilaterals

A group of quadrilaterals in which the opposite sides are parallel and the other is not parallel to the opposite sides is called a trapezoid.

Two groups of quadrilaterals with opposite sides parallel to each other are called parallelograms.

A parallelogram with equal adjacent sides is called a rhombus.

A parallelogram with a right angle is called a rectangle.

A rectangle with equal adjacent sides is called a square.

A special quadrilateral is a quadrilateral that has a characteristic (prescribed shape, separate name). Includes: parallelogram, rectangle, square, diamond, trapezoidal.

A closed plane figure or three-dimensional figure enclosed by four line segments that are not on the same straight line is called a quadrilateral, which is composed of a convex quadrilateral and a concave quadrilateral. The quadrilateral obtained by sequentially connecting the midpoints on any quadrilateral is called a midpoint quadrilateral, and the midpoint quadrilateral is a parallelogram.

The midpoint quadrilateral of a rhombus is a rectangle, the midpoint quadrilateral of a rectangle is a rhombus, the midpoint quadrilateral of an isosceles trapezoid is a rhombus, and the midpoint quadrilateral of a square is a square.

Special quadrilaterals include:

Parallelograms, rectangles, squares, diamonds, trapezoids.

Refers to a quadrilateral shape that has characteristics (prescribed shape, separate name).

The properties and theorems of special quadrilaterals are as follows:

Quality. The circle is complemented diagonally by the quadrilaterals.

Any one of the outer angles of the circumscribed quadrilateral of the circle is equal to its inner opposite angle.

The sum of the products of the two pairs of opposite sides of the inscribed convex quadrilateral of the circle is equal to the product of the two diagonals.

Decide. If the diagonal complementarity of a quadrilateral is complementary, then the four vertices of this quadrilateral are on the same circle.

Rectangles, diamonds, and squares are called special bead parallelograms, and their properties and judgments are:

Moment Retrocardiform Properties:

The four corners of the rectangle are all right angles. The opposite sides of the rectangle are parallel and equal. The diagonal lines of the rectangle are bisected and equal to each other.

Rectangle Determination: <>

A parallelogram with an angle that is a right angle is a rectangle.

There are three corners that are right angles, and the gyrolaterals are rectangular.

A parallelogram with equal diagonal lines is a rectangle.

Properties of the rhombus:

The four sides of the diamond are equal and the opposite sides are parallel. The diamond shape is equal diagonal. The diagonals of the diamond are bisected perpendicular to each other.

Determination of the diamond.

A quadrilateral with equal sides is a diamond. There is a group of parallelograms with equal adjacent sides that are diamonds. A parallelogram with diagonal lines perpendicular to each other is a diamond.

Square nature.

The four sides of the square are equal, the four corners are all right angles, and the opposite sides are parallel. The diagonal lines of the square are bisected perpendicular to each other and equal.

Square Judgment:

There is a diamond leak with a right angle and the leakage sensitive shape is a square. There is a set of rectangles with equal adjacent sides that are squares.

What is called a quadrilateral is defined as follows:

A closed plane figure or three-dimensional figure enclosed by four line segments that are not on the same straight line and do not cross each other end to end in turn is called a quadrilateral.

The definition of quadrilateral clearly states that if it is a closed figure, the proposition in the question lacks conditions. Therefore, this proposition is false.

Extended Information: Classification of Quadrilaterals:

1. Convex quadrilateral.

The four vertices are in the same plane, the opposite edges do not intersect and make a straight line on one side, and the other edges are on the same side.

2. Concave quadrilateral.

The four top points of the concave quadrilateral are in the same plane, the opposite sides do not intersect and make a straight line where one side is, and some of the other sides are on the opposite side.

Nature of the quadrilateral:

Quadrilaterals do not have the stability of a triangle and are prone to deformation. However, it is precisely because of the unstable mobility of the quadrilateral that it has a wide range of applications in life, such as stretching doors and other stretching and folding structures.

Properties of parallelograms:

1) The midpoint of connecting the sides of any quadrilateral is a parallelogram.

2) The area of the parallelogram is equal to the product of the base and the height.

3) Passing through the straight line at the intersection of the diagonal lines of the parallelogram, dividing the parallelogram into congruent two-part figures.

4) A parallelogram is a centrally symmetrical figure, and the center of symmetry is the intersection of two diagonals.

5) The parallelogram is not axisymmetric, but the parallelogram is a centrally symmetrical figure. Rectangles and rhombuses are axisymmetric figures. Note: Squares, rectangles, and diamonds are also a special type of parallelogram, and all three have the properties of parallelograms.