② Properties: Diagonal equality, opposite sides equality and diagonal bisection.
③ Judgment: Two groups of opposite sides are parallel (or equal), and one group is parallel and equal.
The following definitions and properties include the properties of parallelogram. (except trapezoid)
Diamond definition: a group of parallelograms with equal adjacent sides.
Properties: Four sides are equal, diagonal lines are perpendicular to each other, and no diagonal line bisects a set of diagonal lines.
Judgment: Quadrilateral with equal sides and parallelogram with perpendicular diagonals.
Definition of a square: a group of parallelograms with equal dexterity and one angle at right angles.
Properties: Four sides are equal, four corners are right angles, diagonals are equal, and they are equally divided, which is called bisecting a set of diagonals.
Judgment: A set of rectangles with equal adjacent sides, a rhombic square with right angles.
Trapezoidal definition; A quadrilateral whose opposite sides are parallel but not parallel.
I have only learned the nature and judgment of isosceles trapezoid. Here is just the definition of trapezoid. )
Definition of rectangle: a parallelogram with a right angle.
Property: All four names are right angles and diagonal lines are equal.
Judgment: A quadrilateral with three right angles and a parallelogram with equal diagonal lines.
I made all these myself. They should be complete! Note that a square is not only a special rectangle, but also a special diamond. Once I made a mistake, because I was not sure whether this square was a special diamond. Rectangular, rhombic and square all have the nature of parallelogram, but they cannot be judged by parallelogram.