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Parallelogram properties:

1 The opposite sides are parallel and equal.

2 diagonal lines are equal

The two diagonals are equally divided.

4 center symmetry

Parallelogram judgment:

1 Two groups of opposite sides are parallel to each other.

The two groups of opposite sides are equal respectively.

A set of opposite sides are parallel and equal.

4 The two diagonal groups are equal respectively.

The five diagonal lines are equally divided.

Diamond properties:

1 parallel to the opposite side? Four sides are equal.

2 diagonal lines are equal

3 Two diagonal lines are bisected and perpendicular to each other? Each diagonal bisects the diagonal.

4 both central symmetry and axial symmetry.

Diamond decision:

1 A set of parallelograms with equal opposite sides is a diamond.

The parallelogram with vertical diagonal is a diamond.

A quadrilateral with four equilateral sides is a diamond.

Properties of rectangle:

1 The opposite sides are parallel and equal.

All four corners are right angles.

The two diagonal lines are equally divided and equal to each other.

4 both axial symmetry and central symmetry.

Determination of rectangle (rectangle);

1 A parallelogram with right angles is a rectangle.

A quadrilateral with three right angles is a rectangle.

A parallelogram with equal diagonal lines is a rectangle.

Nature of the square:

1 parallel to the opposite side? All four sides are equal.

All four corners are right angles.

3 Two diagonal lines are equally divided and equal to each other? Each diagonal bisects the diagonal.

4 both axial symmetry and central symmetry.

The trial in the square:

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

Diamonds with right angles are squares.

A quadrilateral that is both a diamond and a rectangle is a square.

(In fact, it is not difficult to find that the nature and judgment of diamonds and rectangles are based on parallelograms, while the nature and judgment of squares are based on diamonds and rectangles. Our teacher once said that "diamonds are the most special high-end goods, and half of them are basically difficult to follow in high-end cars ...")

The Nature and Judgment of Trapezoids: A group of quadrilaterals with equal opposite sides are trapeziums. ...

Characteristics of isosceles trapezoid;

1 parallel bottom? isosceles

Two angles on the same base are equal.

The two diagonals are equal.

4 axis symmetry

Determination of isosceles trapezoid:

1 isosceles trapezoid is isosceles trapezoid.

A trapezoid with two equal angles on the same base is an isosceles trapezoid.

A trapezoid with equal diagonal lines is an isosceles trapezoid.