1.

Definition:

Two groups of parallelograms with parallel opposite sides are called parallelograms.

2. Nature:

(1) If the quadrilateral is a parallelogram, then the two opposite sides of the quadrilateral are equal.

(abbreviation for "the opposite sides of a parallelogram are equal")

(2) If the quadrilateral is a parallelogram, then the two opposite corners of the quadrilateral are equal respectively.

(Simply described as "parallelogram diagonal is equal")

(3) The parallel lines sandwiched between two parallel lines are equal.

(4) If the quadrilateral is a parallelogram, then the two diagonals of the quadrilateral are equally divided.

(Simply described as "the two diagonals of a parallelogram are equally divided")

5] A parallelogram is a figure with a symmetrical center, and the symmetrical center is the intersection of two diagonals.

3. Judges:

(1) If two opposite sides of a quadrilateral are equal, then it is a parallelogram.

(Simply stated as "two sets of quadrangles with equal opposite sides are parallelograms")

(2) If a set of opposite sides of a quadrilateral are parallel and equal, the quadrilateral is a parallelogram.

(briefly stated as "a set of quadrilaterals with parallel and equal opposite sides is a parallelogram")

(3) If two diagonal lines of a quadrilateral are equally divided, then the quadrilateral is a parallelogram.

(In short, it means that "quadrilaterals with diagonal lines bisecting each other are parallelograms")

(4) A quadrilateral is a parallelogram if its two opposite corners are equal.

(Simply stated as "two groups of diagonally equal quadrilaterals are parallelograms"

(5) If two opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.

(Simply stated as "two groups of parallelograms with parallel opposite sides are parallelograms")

The Nature and Judgment of Rectangle

Definition: A parallelogram with a right angle is called a rectangle.

Properties: ① All four corners of a rectangle are right angles;

② The diagonals of the rectangles are equal.

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Note: A rectangle has all the attributes of a parallelogram.

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Judgment: ① A parallelogram with right angles is a rectangle;

② A quadrilateral with three right angles is a rectangle;

③ Parallelograms with equal diagonals are rectangles.

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The nature and judgment of rhombus

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

Properties: ① All four sides of the diamond are equal;

② Diagonal lines of rhombus are perpendicular to each other, and each diagonal line bisects a set of diagonal lines.

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Note: A diamond also has all the attributes of a parallelogram.

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Judgment: ① A group of parallelograms with equal adjacent sides are rhombic;

② A quadrilateral with four equal sides is a diamond;

③ Parallelograms with diagonal lines perpendicular to each other are rhombic.

(4) A parallelogram whose diagonal bisects a set of diagonal lines is a diamond.

The Nature and Judgment of Square

Definition: A group of parallelograms with equal adjacent sides and a right angle is called a square.

Properties: ① All four corners of a square are right angles and all four sides are equal;

② The two diagonals of a square are equal and equally divided vertically, and each diagonal is equally divided into a set of diagonals.

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Judgment: Because a square has all the properties of parallelogram, rectangle and diamond, there are three ways to judge a square.

A parallelogram with four equal sides is a square.

② A set of equilateral rectangles is a square.

Diamonds with right angles are squares.

Definition of trapezoid and special trapezoid

Trapezoid: A set of quadrangles with parallel opposite sides and another set of quadrangles with non-parallel opposite sides are called trapeziums. (A set of quadrangles with parallel and unequal opposite sides is called a trapezoid. )

Isosceles trapezoid: isosceles trapezoid is called isosceles trapezoid.

Right-angled trapezoid: A trapezoid whose waist is perpendicular to the bottom is called a right-angled trapezoid.

Properties of isosceles trapezoid

1, isosceles trapezoid with isosceles parallel base;

2. The two angles of the isosceles trapezoid on the same base are equal;

3. The diagonal lines of isosceles trapezoid are equal;

4. The isosceles trapezoid is an axisymmetric figure with only one axis of symmetry, and the vertical line at the bottom is its axis of symmetry.

Determination of isosceles trapezoid

1, isosceles trapezoid is isosceles trapezoid;

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

3. A trapezoid with equal diagonal lines is an isosceles trapezoid.